Why? Just--why?

This isn't a problem so much as--puzzling. I've never seen my cats do anything like this before, and I can't help but wonder if this is going to be a prelude to something that is  a problem.

Let me explain. Our household has six cats (Momma, Spot, Ra, Princess, Asia, and Slipper), and four humans (me, AWM, IB, and RB). Yesterday AWM and I went shopping and one of the things we got was a new areal rug for the living room. We brought it home, took the old one out, and put the new one in its place. (Naturally, the cats were outside while we did this.) After the new rug was in place the cats did something odd. (All of them did it--just not at the same time.) A cat would sniff the rug, go over to the couch, and then flip its tail up before rubbing it's bottom against the side of the couch. (In the exact same place every time.) There was no fecal matter on the couch after they did this, there was no wet spot, and nothing's glowing in the blacklight. 

After the strange behavior the cats have taken no more notice of the new rug, and that leads me to ask--why? What is the purpose of this behavior? What's going on?

I'm guessing here, but (1) it's something new and (2) it has a different smell. So, they are cats and are curious. Rubbing is marking his/her scent on the new "invader".

I'm guessing that the new rug smell worried them, so they felt the need to state their 'ownership' of the room in a slightly more dominant fashion. You could try getting scent cloths from all of them (as used in introductions - take a cloth for each cat and rub them all over with it, focusing on cheeks and jaw) and rub the cloths over the rug - maybe even then leave the cloths scattered on the rug overnight. This may help to counteract the strange new smell and help them feel that the rug belongs in their territory. Spraying it with Feliway or Comfort Zone wouldn't hurt either.

Hopefully this will head any unwanted behaviours off at the pass.

This would make sense--if the couch  was new. We've had that couch longer than we've had cats. Why would they feel the need to mark territory they're already familiar with?

Tallyollyopia said:

 
This would make sense--if the couch  was new. We've had that couch longer than we've had cats. Why would they feel the need to mark territory they're already familiar with?

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the couch is higher up than the rug so the scent they leave behind would "come at you sooner" I'd think. it could be also that the couch is more familiar than the rug so they are showing their preference for an old friend over a new intruder. who knows? they are mysterious creatures 

They certainly are. They amaze me all the time.