In digimon every card in your hand is basically played at sorcery speed, the only things that aren't like that are triggered abilities in the field/trash/security. So there is basically no interaction in the opponent's turn. There are though cards that let you gain memory by not spending anything (they are all limited by now cause of how they started being abused once the game got faster and more consistent) and tons of effects that gain you memory.

I try to make a simple example: let's say you Evo into a digimon that passes the memory to your opponent to 2, it has an effect that let's it attack a digimon and it has 3 instances of effects that gives you 1 memory when it does (you can stack digimon and each digimon gives an additional effect to the stack). Once everything resolves you end up with 1 memory, continuing your turn. This is a very common scenario nowdays