I'm somewhat confused from your question.
The general rule and i don't think this is defined by game style but rather the game architecture itself, is that rendering(animations) should happen independently in your game. And the switch between animations should be triggered by state changes. If you arrange your game architecture like this then it's only a matter of when a state change is triggered.
I hope i did provide some insight.
Edit: updated with more info.
You have to change your point of view on this matter. When you are saying that this type of game doesn't have many animations, you should really be thinking about the game/object state changes, which in such a type of game is usually correct, many things remain static for extended periods of time.
I will try to give you a very brief example of how a state change interacts with animations but really, you should further look this up on the net. Maybe check how animations are handled in general.
So in my example i have a player object/class with a private member named current_state of type PLAYER_STATE. PLAYER_STATE could be an enum could be class, how you architecture your game is on you. I prefer to use enums.
Now you should probably have some kind of system to handle your animations. And that system would check on the players state (current_state) to see what action is the player currently performing and re-adjust your animation(frame sequence for sprites) to the one corresponding to the action that is stored on your player (IDLE, RUNNING, JUMPING).
I hope i gave you an idea but really, this is an extended topic that needs further research.