Hey,
I have a camera with HDD inside.
I recorded some video and when I watch it on the camera, it's nice and clean.
When I copy his files on the computer and watch it in Premiere or After Effects, they become jitterish.

Is it because of a lack of a codec or somehow ?

No, it sounds more like your computer is not up to the task.

AVCHD files are extremely comressed and need a lot of computing power just to be played back, let alone edited.