Hi
You have basically two option on VPN tunnel: Split tunnel or tunnel all. Tunnel all means that all traffic will be sent to the firewall.
Split tunnel means some traffic is sent to firewall and some traffic is sent locally.
Let´s say you are using the VPN from your home. With tunnel all, all traffic will be sent to the firewall. Let´s say this is a corporate VPN and the firewall is placed on the Company DC. Then, all your traffic goes to the company DC.
With splict tunnel you can device. Maybe internet traffic you can send locally through your ISP and Corporate traffic you can send through the VPN to your company DC.
But keep in mind that this is all made on Firewall and not on the Anyconnect app. If you dont admin the Firewall, then you need to talk to the guys who does. And this is usually a Corporate decision, not a user devision.
On you case, when you connect to the VPN, if you run the following commnad in your machine:
nslookup www.google.com
Who resolve google.com for you. Which DNS server? Can you share the output?
