If a card is legal in the current format, then any print of that card from an older set may be used. In your case, Evosoda from Generations is an exact reprint of the XY card, therefore you can use it in a Standard deck next season. You can even use Switch and Double Colorless Energy from the original Base Set in a standard deck, even though Base Set has been out of the format for over a decade! If it's in a currently legal set, you're generally good to go. This applies not only to Trainer cards but also to reprinted Pokemon and Energy cards (Note that it doesn't matter if the art was changed; as long as the card name, effects, attacks, etc. are the same the card is legal).
Please note that there are a handful of cards which have received erratas since their original print, such as Pokemon Catcher, which did not originally require a coin flip. For these cards, you will sometimes (though not always) need a reference card -- that is, a print showing the current effect, to keep to the side of your play area. For example, if you have four Pokemon Catchers in your deck, you can use four of the original print from Black and White (or the Secret Rare if you wanted to show off), while keeping an XY Pokemon Catcher with the current effect to the side as your reference.
Also note that in Expanded play, you cannot use the original Base Set Computer Search; you must use the Boundaries Crossed ACE SPEC version. The reason for this is the card received a major errata and would require a reference -- but since you can only have one ACE SPEC in your deck, you may as well just use the current one.
I hope this was helpful!
