i would just try to check what areis your nat table(network routes) in Windows when you connect via Cisco VPN. the VPN app just might change your nat table and adjust all traffic to go only via VPN adapter.
just open cmd as admin-> "route print"
it should list you Nat/route table, you start off that
You can also convince your IT person to disable "Tunnel all" on the VPN setup, unless its PPTP, of course. But even if its PPTP just say your IT to change it asap as its insecure.