When I'm connected through VPN to the Internet Archive (public domain) site and start a download there is no data transfer started in Tixati until I close my VPN connection.
Is there anything that can be done to correct this?

I'm pretty sure it's your VPN provider that doesn't allow torrenting. I guess you're using a free VPN service. They don't allow torrenting.

VPN usually works just like this. So, you should be aware that it's gonna be like that.