The “weird zoom trick”, where the background seems to either be sucked towards the camera or pushed away, is done using a combination of zooming-in whilst moving the camera away from the subject (or vice versa). The results of this basically mean that the subject remains still in shot, while the background moves. This technique is an excellent tool when used effectively, however it is harder that it seems to do well.
This technique is also known as “blowing out the background” and has been a popular suspense-building technique in suspense and horror movies. Hitchcock was one of the first to use this, although there are good examples in Jaws and Goodfellas (extremely slow). The technique is even parodied in the Kevin Bacon film The Big Picture, giving weight to the brief that its use is pretty clichéd these days.