There's two things to point out.
First of all if you do packet tracer you would actually have to simulate the traffic as coming from outside interface.
In regards to your URL, it seems like you haven't defined any DNS servers on the management of the ASA?
Have you made sure the server is reachable from the Anyconnect Profile you're connecting to? Is the profile split tunneling or full tunnel?
Have you specified a DNS server for the connection profile as well?
Connected to the Anyconnect client, you can also see the routes being injected into the client by going into the route section of the client.