Normally, you need to buy a ticket from/to the tariff border point. The location of those points can be in a real station (such as Brenner, Tarvisio or Chiasso) but can also be a virtual tariff point, such as Ventimiglia(fr). You can often see these virtual tariff border points in the planner.

To add a journey to a mobile pass from/to a virtual tariff border point, you have to add a manual journey to My Trip. However, the iPhone app has a long-standing issue with manual journeys (they make all journeys invisible on the same travel day) so do not add manual journeys if you have an iPhone, but use the first station abroad instead.

Thank you very much for the clear and quick reply. It happened to me in the past though, that I had a ticket to Brenner and the Austrian conductor made me buy a further ticket to Innsbruck, claiming that Brenner is in Italy and therefore I was trying to cheat and travel without a ticket (despite me having already added a day of travel on my pass from Brenner to wherever I was going). He was quite annoyed that I didn’t have one and made me feel quite embarrassed actually.
That was a paper pass and now that I am using the mobile pass for the first time I want to make sure I know how to deal with this recurring issue.
I stand by my case that this whole thing regarding tariff border points, that you perfectly explained, should be made clearer on the Interrail website, and should also be explained to train conductors.
Also, I just checked on the planner app, and neither of these stations (Brenner, Tarvisio, Chiasso, Ventimiglia) shows as a virtual or tariff border point. Isn’t that something that should be improved? I find it quite important.

In the planner, I do see Ventimiglia(fr) if I open the train details. E.g. ask a journey Ventimiglia - Nice and then tap on the train number, so you see all train stops.

As to Brenner: the border is in the station and the northern part of one of the platforms is in Austria, so you could well argue that this station is in both countries.

Thank you again for your help! I had a look again and for Ventimiglia I see three options: France, Italy and Frontiere (border). So in this case it is quite easy to know how to operate. If I travel into France on my Interrail, I just choose Ventimiglia (Fr) and problem solved.
But in the case of Tarvisio, for instance, there’s only one choice (Tarvisio Boscoverde, Italy). Effectively I would be travelling without a ticket for a few kilometres. And if I start the Interrail trip in Tarvisio, I would be using up the outbound trip.
This whole thing is honestly very confusing. I don’t see why there couldn’t be a grace zone of 20-30 km from borders where Interrail pass holders can just travel without having to always wonder how to proceed. Or the app should have a “split-list” (for lack of better words) of border stations. For instance why not have on the app an option for Tarvisio (Italy) and Tarvisio (Austria), just as is the case with Ventimiglia, so there’s no longer any misunderstanding, and entering a trip becomes a lot easier.

PS: “As to Brenner: the border is in the station and the norther part of one of the platforms is in Austria, so you could well argue that this station is in both countries” ...I tried to argue that with the conductor and it didn’t go down very well!

You could always add a manual journey and choose as a starting point e.g. Tarvisio Boscoverde and then select Austria as the country. Then the pass shouldn't complain about your country of residence.

My impression is that this has all not been very well implemented. I recently saw a complaint of someone using the one country pass for Switzerland (this was in the Facebook group). SBB have a very clear map of Interrail validity and that includes a few stations outside of Switzerland, such as Domodossola or Konstanz. But the mobile pass wasn't having that.

I have seen this happen before. The One Country Pass for Germany includes Verona for instance, but even train conductors seem puzzled.
I agree that this is not properly implemented. And longer passes should have a couple more inbound-outbound trips included (say three trips for the three-month pass) just to make things fair for those who live far from the border.

I used a paper pass in 2019 and 2018 between Brenner and Innsbruck and it works, the ÖBB train conductors looks on it very long, but they said nothing. Because i would have them told to look at the ÖBB tariff handbook.

But for both trips I used the S-Bahn and the REX and not the Eurocity. 

About the One Country Pass, yes it is valid also on some train to Italy, but not for Italians. The same thing happens to the One Country Pass Benelux, when you are from The Netherlands, you can’t use it at all in The Netherlands. 

It should exist a Pass Ticket/Reservation sold only at DB/ÖBB Ticket offices or maybe also at Trenitalia, where you have to pay only for the Italian Part. This would be maybe the correct ticket?

Partial Pass or something like that

You could also ask directly via Facebook or Twitter direct messeging to ÖBB or Deutsche Bahn if they can confirm to you, that you can use Interrail from Brenner without a outbound/inbound. 

Some older points: Ventimiglia_ the point as for now is that ONLY local TER SNCF trains run from Ventim (stazione) to FR and its even IMpossible to buy tickets to the official right way for this. SNCF simply accepts any local French tickets without chasing these people for the 1 or 2 Kms (on a longer trip the tariff would be the same anyway) they cover in la bella Italia (con multo scioperta).

Brenner/Brennero IS an offical shared tariff point, as even the local VVT has it in its farebook. AT=Austria has many of these stations (which is not very usual), also Salzburg and Passau toward DE and even as far as Lindau and Fehring and Hegyeshalom to HU.

Same applies to Chiasso, it doubles as both CH and IT stazione/point.

Problem for Italiano here is that TrIt is restricted to only serve domestic stops and cannot handle anymore single tickets to borderposts. As is also the case (more or less) for BElgium-but the belgians have far higher tariffs for even same nr of KMs to borderpoints as they find its INTERNational.

Thanks everyone for your insightful replies. This helps a lot. I still think there needs to be more clarity--after all I am a passenger who should be informed as to where his ticket is valid. I am not supposed to have a tariff handbook for every country. 
I think this would be easily solved if the Rail Planner app, under the “Rail Network guides” section, had for each country a detailed list of entry points. All we need to know is whether each entry point counts as domestic or international, and considering that most countries in Europe have no more than four or five railway border stations, this is something they can fix in two working days... 

Ok, an update. I am currently on the Verona-Munich EC train for which I bought a regular ticket from Verona to Brenner with Deutsche Bahn.

The idea was to travel to Brenner on a regular ticket and then use the Interrail pass from Brenner to Munich and onwards.

I added the Brenner-Munich leg on my Interrail app, and the app is saying that I need to use up my outbound journey.  That's for about two meters of rail travel.

That's exactly what I suspected would happen. What a pile of junk this mobile pass is. I already regret not having bought the paper pass, which at least allows you to force these limitations. 50 years of Interrail and still they haven't figured out how to handle these border crossings.

Do you have an Android phone? Then add a manual journey Brenner - München Hbf and place Brenner in Austria.

On iPhone, there still a bug triggered by adding a manual journey, so I wouldn't risk that.

And of course, this is again bad implementation of the border tariff points.

@Felipe.iturrieta @Leo could you please look into this?