It’s kinda weird. It's true that you don’t need a reservation on some of these international trains from Italy, but you do need to pay a supplement. You can sometimes pay it on board if you like, or do it in advance which is likely to be cheaper.

Which route are you looking at?

Do you know how much it would be to pay before compared to paying on board? Also, how would I pay beforehand online? Thanks 

It depends on the exact route, there are lots of options.

If you go via Zurich, for example, Milan to Zurich is €11/ 13, booked online at oebb.at, including a seat reservation. No compulsory reservations on Swiss trains or Railjet

via Verona to Innsbruck is €10/ €15 and you can pay on-board, or you can get the supplement (and an optional seat reservation) at oebb.at. You would also need a reservation on the Frecciarossa from Milan to Verona.

via Tirano over the Bernina Pass has no supplements or reservations except for some some Panorama trains 

There is also Night Train from Milan, and other routes via Slovenia, so it would help if you post your exact route and trains you will take.

This is the journey I’m planning on from Milan-Salzburg. A supplement is only required for Verona-Innsbruck right? 
 

Also, I know the chnage over is long, I put it as a filter to be 2+hrs so I can stop on some more places so don’t want to change this.  

Yes, just the Verona-Innsbruck needs a supplement. It's €10 in second class or €15 in first (if you have a first class pass). You can do this in advance, or just pay on the train. 

On all three trains, you can turn up without a reservation.  If you want a seat reservation as well, you can do it (for the second and third train, but not the regional one from Milan) on oebb.at for €3 for each train.

-

Edit: I’ve checked a bit more, and it might be that you pay an extra €5 if you want to pay on the train. So it would be better to get it in advance.

https://www.interrail.eu/en/plan-your-trip/reservations/trains-with-additional-supplements

Brilliant, thank you! Is there a route that I could take without having to pay any extras? 

Yes, you could go from Milan past lake Como to Tirano and then over the Bernina Pass into Switzerland. 

The trip over the Bernina Pass is absolutely beautiful. It would be a fairly long trip if you do it all in one day to Salzburg, but doable. I would probably break it over two days. Note that this summer the line between Milan and Tirano has some maintenance, so you will have to take a bus for part of the trip, but this is a short section and included in your pass.

The journey is very well described here. You could take the train as far as Chur, then continue from there to Salzburg. I did this trip last summer, and it was beautiful.

https://www.seat61.com/trains-and-routes/bernina-express.htm

Although the page there talks about supplements, that’s only for the panorama car. You can travel in the ordinary cars, or other trains over the same route, without supplements.

Your route would be Milano - Tirano - Chur - Buchs - Salzburg, and the last direct train to Salzburg leaves Buchs at 1800.

There’s plenty of time to get a train up from Milano to Tirano, and there are lots of trains (some with connections) from Tirano over the pass to Chur.

You can also buy the supplement on cd.cz and get a free reservation with it. Add the Interrail pass as a discount.

I have yet to see any reports from people that they were indeed charged an extra on-board supplement.

You can avoid ECB using local trains RV and R Verona-Brennero and then S-Bahn Brenner-Innsbruck, from there RJX to Salzburg. But you need to change more often and it takes longer.

Do you know how to book the supplement at oebb.at? I can only find the seat reservation.

tickets.oebb.at, do NOT use "seat reservations only” but add the Interrail/Eurail discount and then select "One-way tickets and day tickets”.

Oh I just found the answer to my own question. If anyone is looking how to get the supplement on oebb.at, this person here explains it very well:

The strange thing with this is if on obb site you add interrail discount and search Verona - Brenner (or other Italian destination) tickets for the OBB EC service it tells you you already have a valid ticket and just offers seat reservation for €3. Only when tickets for crossing the border to an Austrian/German destination are searched for does it add the €10 surcharge.

I did this recently and when the ticket checker came along and tried to get €15 from me I pointed this out and he backed off.

The rule is for rides to/from and IN Italy. Because DB/ÖBB gets no money or less money for the italian part by Interrail. 

Thats a bug of the ÖBB Ticket Website.

If that's the case, then that's their own fault.

It sure is, but from a customer's point of view, a railway can't ask money if their system works like this.

OBB’s website bugs and their revenue issues are none of my concern, it’s their website, if they want the supplement then it’s entirely within their remit to fix it.

You simply cannot state no charge on the website then when the journey has commenced demand payment.

Inportant is what their terms of use says. Here on their ÖBB Italia Website they say it clearly. https://www.obb-italia.com/de/angebote/interrail-eurail 

An example: Some people check ÖBB booking website where the Klimaticket Ö is included outside Austria. There was a bug, that the EC/IC/RJ on Salzburg-Freilassing (Germany) are also included, but on this route only S-Bahn is included. What the booking website says can be right, but has no legal meaning. 

Don’t get me wrong, I’m not a fan of this fee. But the rules are clear. And this bugs should not exist, this is is not what you expect from a railway company like ÖBB.

What they do not write is about the 2,30€ fee on the Eurocity Trieste-Ljubljana(-Wien), the booking website of ÖBB say to pay. The website or the term of use of ÖBB Italia do not mention it. 

P.S. the fee will cost 3€ more on board of the train on trains of ÖBB Italia (RJ Venezia-Wien; no fee on RJX Bolzano/Bozen-Wien) term of use ÖBB Italia E.1.1.

https://www.oebb.at/static/tarife/de/handbuch_fuer_reisen_mit_der_oebb_in_italien/index.html

At DB-ÖBB Eurocity 5€ (at 2.9. of the term of use of DB Italia) more. https://www.obb-italia.com/dam/jcr:41e86bcc-62dc-48cb-b504-c79b46c392b9/befoerderungsbedingungen-de.pdf

I still have to see the first report from someone who actually had to pay this extra on-board fee.

Yeah, Trenord staff will not ask it. DB staff do not sell on board anymore, maybe on DB-ÖBB EC it is still possible. ÖBB asks 3€.