What you do on a browser besides Tor Browser Bundle (TBB) does not affect what you do on TBB.
For example: You google how to eat cats on Tor Browser Bundle. Then you close TBB and open up Firefox. In Firefox you google how to adopt cats. The people watching know you are trying to adopt a cat. They also know someone is trying to eat cats. They have no clue that you are both of those people.
To get anonymity throughout your computer please use Tails.
Tails is a live operating system, that you can start on almost any computer from a DVD, USB stick, or SD card. It aims at preserving your privacy and anonymity, and helps you to:
- use the Internet anonymously and circumvent censorship;
- all connections to the Internet are forced to go through the Tor network;
- leave no trace on the computer you are using unless you ask it explicitly;
use state-of-the-art cryptographic tools to encrypt your files, emails and instant messaging.