JPA in is not threadsafe, that means that you must use the entity manager and do all modifications until you commit the changes on the same thread. Only ways to guarantee that with an actor is to do complete transactions in the same actor (you should not be sending mutable state between actors anyway, which kind of rules out passing JPA entities between actors for mutating them).
Another option could maybe be to use the pinned dispatcher, to have one actor that will always run on the same thread and can safely do a transaction on the same entities over a number of incoming commands. But I think the first option is a better idea.
Not sure if there is anything additional about Spring Data that would be problematic. I know that some other Spring modules store context-like things in
ThreadLocal which does not work with actors since they do not all execute on the same thread.