To really be a law abiding visitor, write the date of travel before boarding said train.
Waiting until the conductor (Capotreno) inspects the tickets is completely illegal and if the Capotreno who finds you doing that or not having completed the date is doing their job properly they will cross out the empty or just completed box and write the date in the next box for you - unless they suspect you of trying to evade the use of the pass in which case things can get very nasty.
Now, for the advice to get on the train and write the date on "before the conductor comes around" is, in my mind as a professional railway man who is quite knowledgeable about European trains and passes from an operational point of view - - that's pretty dodgy. As soon as you step on the platform you are within the ticketed area and that date must have been completed before you enter the ticketed area.
Read the terms and conditions which came with your pass - carefully.
I wouldn't want to have you feeling encouraged to wait until you see the Capotreno in the next car in case you might hop off at the next station before being checked so you don't "use" a day. Sometimes on Italian trains tickets are checked by a team who are spread around the train. As I said, if they think you are evading they will become no end of nasty and your day can be well and truly spoiled.
Now, Reed, I in no way think that any of that would apply to you. The reason I write what I write is because of the earlier advice given by a railways and passes expert of the institution supporting all this wonderful travel.
Please follow the rules and put the date on the date box prior to entering the ticketed area.
AND, yes, with a suitably dated pass, you just hop on and off both Regionale and Regionale Veloce trains to your heart's content.