The "This counts as evolving" wording means that you would do anything else that is included in evolving, like removing status.
Normal gameplay rules do state you cannot evolve turn 1, however in almost all card games, if a card overrides the basic game rules, the card take precedence (provided the card is not errata'd)
Back a few formats ago, we had a supporter names Wally's Training. That card allowed us to search our deck for a pokemon card that evolved from your active pokemon and evolve it (This counts as evolving that pokemon).
If you did Wally's training first on a squirtle to get a wartortle, on the same turn, you could NOT evolve to blastoise, because the wartortle is not eligible to be evolved.
HOWEVER if you evolved to wartortle normally, then played Wally's training, that WOULD work, because the card supersedes the normal gameplay rules.