When you move your mouse, you have to move your mouse in the opposite direction to reset the joystick, or put down the controller.

How to reproduce:

1. Get a Tweaked controller
2. Press "Grab Mouse Movements" and move your mouse without moving it back.

This could also just be a setting put it is very annoying when trying to aim something with your mouse.

This is working as intended.
Use the "Use velocity instead of position" setting if you want it to behave differently, or alternatively you can reset the virtual cursor's position using the "Center mouse cursor".
See the wiki page about it, everything is explained: https://github.com/getItemFromBlock/Create-Tweaked-Controllers/wiki/Tutorials-on-the-advanced-mode#configuring-the-mouse-cursor-as-input