Hi jaught,
Thanks for test project! I saw same behavior you described in your project, and determined cause is Add Actor Local Offset node. It appears to not be working correctly on Clients, and it has nothing to do with ReplicateMovement setting. You can get around this by using different movement methods, such as Add Movement Input (which is what I originally tested with, and can verify works on Clients).
I’ve entered a bug report for issue (UE-13071), and I’ll let you know as soon as I see an update on it. Thanks again!