tl;dr : positions for imported anims/FBXs are inconsistent and make anims unusable when played.
For some reason, when I initialize my T-pose, or import any animation, the character is never in the middle of the grid, it even has a different position for every animations, and when I play them, the character spins around like it's in a tornado. I could fix that by hand, but it would take avery long time, and GGT is made so we do not have to waste this time.
So far, it seems that I am having this issue only when the mesh was exported from mixamo without skin (only for the animation).