Does it mean that we are, potentially, on one of two poles(?) of the observable universe, if we're observing most galaxies around us rotating a certain way?
How does cyclones/hurricanes relate to being “on one of two ‘poles’”?
Do you mean hemisphere?
The important part is that at any given point on the elastic strip, both sides are getting further away. Everything else is getting further away.
You might think if A-B-C-D are points on the tape and A-B are expanding and C-D are expanding, then B and C must be squished together, but the distance between them is also expanding. You have infinite elastic, but you also have infinite room to stretch it (even along the direction it already occupies). You now have A--B--C--D.
It's tempting to think about that stretch from the point of view of the floor/table beneath the elastic, in which case some parts of the elastic move faster than others as they stretch, but if you always think from a point on the elastic, then the speed of the rest of the elastic depends on how far away it is. Stuff twice as far away moves away twice as fast. Stuff infinitely far away moves away infinitely fast. That's true for every point on the elastic. No bunching up.