No, this is Italy-the land of the many delays (ritardi!). THAT date is when the summer timings start=a big hurdle. But again-it has been said here so many times: there is no need for panick so long ahead-most REServations only are done a few days advance only and trains are only really full 100% a very few odd dates in the yr.

PLus that TrIt does NOT start from Nice, thats ugly outlandish foreign territory for them and they only want to do Inland-that means local train (UNreserved all the time) to Ventimiglia then from there. OR use the always UNreserved regionale trains onward-change Genova.

PLUS-as has also been explained here a few dozen times now-you canNOT just REServe seat on site of trIt. There is a sneeky way around this via Austrian railway=Oebb.at- just find the advice in this forum.

Welcome to the wonderful world of how these burocratic state institutions treat their valued customers.

Thank you so much for your reply.  I hear you!   Is there a date when they release the Summer timings?

We’re all waiting for that. Trenitalia have already published their summer timetable (valid from 12 June) on their own website, albeit only for long distance trains. Regional trains (some of which also cover large distances) will probably only be published next month. I'd expect the long distance trains to turn up elsewhere any day now.

Wich station of cinque terre will you go? Because there are a few. Best way from Nice to Cinque Terre is via Regional Trains (no reservation possible, just hop on the train).

TER to Ventimiglia

RV to Genova 

RV direction La Spezia

For the timetable you can look for the timetable some days before 12 June (if you want to go on Sunday look for a Sunday). The trains should run the same like before the timetable change. Special trains Cinque Terre Express run from March to November. 

Timetable till Ventimiglia is online (French part).

You can check via bahn.com or trenitalia.com from Ventimiglia for train connections before 12 of June and then check the train number via e656.net if the train will run also after timetable change. This website is only in italian, but it has data from the italian rail infrastructure manager till timetable change in December. 

Please keep in mind that timetables can change also a few days before, due to works.