I think I can answer this since again, I'm a former player of the game this is inspired from.

When they say turn-based it mean each player takes alternating turns moving pieces on their own board to attack the opponents board. Now that I remember in Primal Legends when it was your turn you could move about 3 of your pieces to attack the opponents board. After you ran out of moves for your turn it was your opponent's turn and they could move 3 pieces on their board to attack you.

But no, no scheduled PvP where you and all PvP participants have to gather at a specific time. The game just match makes with everyone else that is looking for a match at the same time you are looking. Again this is all based on my knowledge of the game they mentioned in the OP.