JSessionID Expiration

You might be confusing persistence with session management. The F5 is going to use your JSESSION value to maintain load balancing affinity to a single selected backend server. Once that persistence record goes away the F5 should make a new load balancing decision. That has nothing to do with how the application and/or server behaves. If the client is still presenting a JSESSION token it's possible that the server (potentially a different server) could be honoring that.