I am trying to understand what could be causing this sort of behavior. In our environment we multiple domain controllers that delegate to the F5 GTM. We set up the GTM to respond to internal queries with internal VIP resources, and to respond to external queries with our Internet facing IPs. However, we started noticing that some of our sites have been flapping between the internal VIP and external VIP when an internal-sourced IP requests a service. Oddly enough this one is happening on only a handful of Wide IPs.
I honestly think this is not so much an F5 issue than an issue with the domain controller doing the delegation to the F5, but I need to be able to prove it, and I am still learning F5.
First make sure the virtual servers are limited to listen on either the external or internal VLANs. It sounds like a routing issue in your network. You can use tcpdump to see on what VLANs the requests are being received. The syntax below will also log the source MAC address.