In windows, the F5 VPN client will attempt to assist Windows in name resolution by:
1- Setting the DNS server on the Network Access VPN adapter OR the main network adapter, depending on if you have "Enforce DNS Search Order" enabled or not in the NA resource.
2- Using the DNS Relay Proxy (it's an optional F5 Windows system service you can start/stop) to proxy client's DNS requests. You will want to try to stop this service and/or start it, depending on if split-routing is set up or not and if you're using split-DNS or not, and/or how you want the client to behave.
3- If 2 fails and the current user has admin permission, it will try to add host entries.
How Windows does DNS (what settings are used, what adapter, routing, fallback options, precedence, etc) is a bit complicated. To understand it, it's best to look at the Microsoft article on the topic:
https://technet.microsoft.com/en-us/library/cc772774%28v=ws.10%29.aspx
Using the commands like ipconfig /all , etc, you can easily see what settings are being pushed by the client into Windows and follow along with the client sections of that document.