Ok I figured something out.
I have a rectangle sprite as player (for collision box). This object has the platform behavior.
To this object I have pinned the player animation (another sprite object). This object is not lagging behind.
So to the player animation I have pinned the accessories, like glasses, hair and so on to its corressponding image point.
This objects are lagging behind, because the aren't pinned to the actually moving object.
If I pin them to the player object having the platform behavior, those objects also stop lagging behind.
Any ideas why this is happening?
Edit: Made an example