Character moving weirdly

Hi,
I'm doing my first steps in humanoid animation logic, and I'm on an issue.
My character is making a little move before stopping, so it slowly shifts from the straight forward axis each time it stops.

The logic is a simple Idle <=> walk <=> run with mixamo clips.

What did i miss ?
thanks

 

Posting some Gif for more explainations.
Each stop the character leaves the Z axis more and more.

Is it in my clips ? my animator transitions setups ?
Moving keys values to more zero centered seems to do nothing.

Cheers