When you use TAILS, only applications that are aware of Tor will be using Tor and other applications just go nowhere.
Tor Browser is a great example for explaining the separation between application layer and network layer anonymity. The tor client gives you network layer anonymity while Tor Browser gives you scrubbing of cookies and anti-fingerprinting. Using another browser, or other applications in general that do not try to provide application layer anonymity, with Tor wouldn't protect against all the application layer attacks and so you end up with less (or no) protection.