How do I configure Tixati to use PIA?

https://www.privateinternetaccess.com/pages/client-support/

Enable port forwarding in the application by entering the Advanced area, enabling port forwarding and selecting one of the following gateways:

Netherlands
Switzerland
CA North York
CA Toronto
Romania
Sweden
France
Germany

After enabling port forwarding and re-connecting to one of the above gateways, please hover your mouse over the System Tray or Menu Bar icon to reveal the tooltip which will display the port number. You can then enter this port into your software.

Configure your router to forward that port to your computer
http://portforward.com/english/routers/port_forwarding/

Then configure tixati with that port (step2)
http://www.tixati.com/optimize/

should work with that configuration

Why exactly would this need to be configured this way?

All I have ever done was connect to my VPN, then launch the torrent app. It has never failed to download, and has never disconnected. Does the torrent app somehow bypass the VPN if it is not configured as above? Please explain.

Usually your router/torrent will use UPNP to configure the port for you.
Since most ISP do not block incoming and outgoing port (maybe except a few specific port), UPNP works well.

with privaterinternetaccess, there are almost no incoming port that are unblocked.
try with http://www.canyouseeme.org/  once connected to your vpn to see the difference.
(Outgoing port should not be affected)

In PIA, once you enable port forward, you get a random port #.
that's why you need to manually set it in tixati while connected in VPN since PIA and Tixati are not set to talk to each other and set the port for you.

Your torrent download will still work without port forward but you probably won't get the same performance.

http://netforbeginners.about.com/od/p/f/What-Is-Port-Forwarding.htm

Also, disregard setting the port forward in the router. You should never do it while connected in VPN. It's a security issue. That was my mistake.

Port forwarding can help optimize downloading.

Also disregard the part about doing the port forward in the router, it's a security issue. My mistake.