The poster frame is an attribute of a chapter point. Setting a poster frame on a different frame than the chapter point is possible – as long as both are within the same timeline – and you will see the poster frame update in the linked button.
When you navigate the timeline using the next/prev buttons, it should go to the next/prev chapter point which you set in the timeline – not the poster frame of that chapter.
So is the problem that it’s really not going to the chapter point you set? Or were you expecting it to go to the poster frame?