Registered to say thanks to @monler and to help others too, just in case someone finds themselves in the same situation. Just got the T3 model and left the red cap on the cylinder thinking it must be part of the chair given no warning stickers were around it etc (which by the way is extremely silly design decision). When realised what had happened was a bit too late as the cylinder was 'set in stone', so to speak. Pulling and wiggling didn't help, so do not bother with that. Will injure yourselves before the thing will move a hairline.
Instead take a hammer, wrap its head with some thick foam (I used exercise mat type of foam) and while pulling the base away from the chair give a few knocks to the base part that connects with the cylinder (just as @monler said). That's the metal ring that wraps around the cylinder top. This should loosen it up and the cylinder will pop out with no damage or marks to the chair. And right there on top you will see the dammed red cap gloriously sitting on the top. The relief is quite unimaginable so hoping this will help someone too!
