Typically the load balancer, in F5 case the BIG-IP LTM, is "publishing" the application (IP) running in the server as a virtual server with a virtual IP address and port. It acts as a proxy (typically as full proxy terminating the TCP level session from the client and creating a new TCP session between the load balancer and the real server). So being inline between the client and the server, all traffic goes through the load balancer in normal case - from the client to the server and responses back from the server. If you add stickyness, the case does not change.
Stickyness or persistence in F5 terminology, is a normal way to keep the client session to the chosen real server, if the application is stateful and needs it to function properly. For HTTP traffic the normal persistence option is to use cookies, so you won't need timer in that case. BIG-IP LTM can create and add the cookie. Source IP (=client IP) persistence can also be used, then there is a idle timeout timer specified. For persistence there are multiple options and mechanisms available depending on applications and protocols used. You can also create your own persistence method based on almost any information you have in the traffic (sc. Universal Persistence). The LTM in between the client and the server farm, will check if persistence is used and keep the traffic going to the right real server.