The front part of the pole wouldn't pull the back part of the pole more so than in any normal contiguous space. If you send a pole flying from the front and catch it mid-flight from the back stopping its motion, you'll have to apply a force opposite in direction to the motion of the pole, and by Newton's third law (every action has an equal and opposite reaction) it's gonna pull you towards the direction it's moving by reactionary force while decelerating.

In the case if moving portals, it might be a bit confusing, but what it comes to teleportation through the portals, the portals are absolutely stationary the world around them moves. And in the case only one of the two portals move relative to the ground, not only does the world move relative to both portals, it also deforms in a non-euclidean manner. That is why the pole that was stationary relative to the ground suddenly started moving after coming out the portal. And yes, it would require massive amounts of energy for the portal to function like that and keep its own momentum relative to the ground after teleporting things, but tbh that's a woe for Aperture science, not mine 🙂