These are know as 'parallax' effects/transitions. There's no preset 'effect' in after effects (or Premiere Pro) to do this - other than manually creating it yourself. You can do something similar in Premiere Pro and there are transition templates available to purchase from companies like motionarray, storyblocks etc.
There are even a few free templates floating around. (search 'free premiere pro templates')
I had a look at both motionarray and storyblocks and they have a few similar effects available for Premiere Pro. Not quite the same but perhaps similar enough.
That said (as Peru Bob pointed out) After Effects will give you much more control and allow you to create your own effects.
And once created you can export a 'mogrt' from after effects to use in Premiere Pro and simply customise with your own footage.