Welcome to Akka.
Firstly, Hazlecast and Akka are not really the same beast. Akka is not "just a cache", it's active entities doing things - i.e. Actors, similar to like Erlang works with processes.
So it may help to change the mindset a bit, since it's not a cache. It can however model very similar (though strictly more powerful) things.
For example for rebalancing and persistence etc you should have a look at:
- cluster sharding (which combined with akka persistence gives you a solid foundation for super scalable event sourcing)
- distributed data (which is picking the opposite trade off, being very fast in memory replicated data).
Happy reading!