It is not the actual tube where the hour or minute hands is fitted, but it is the tube that is directly "inside" the free cannon pinion which in turn is inside the tube of the hour wheel.
The thing is, I was refitting the hands after a repair, when fitting the chrono seconds hand I got it slightly misaligned so I was going to remove and refit it. The quality of the hand was pretty poor and when trying to remove it I broke the "tube" of the hand (I was using the "remove chrono seconds hand ONLY approach", I should've removed all hands using the hand removal tool instead, stupid lazy me).
So, I'm left with a chrono seconds hand tube that is stuck on the pin of the chronograph wheel. Ok, I can't remove the broken tube off the pin from the dial side since the tubes of the hour and minute hands are blocking the access to the pin of the chronograph wheel. So instead I go from behind, remove the auto device bridge and then remove the chronograph wheel, effectively making the broken tube come off of the chronograph wheel pin and get stuck inside of the center tube instead! Ok, at least the chrono wheel is clean, now I only have to get the broken seconds hand tube out of the center tube. I used a broach and tried to push it out of the center tube, it succeeded, but at the same time I actually pushed the whole center tube out through the tubes of the minute and hour hands! Well, not completely out, since I stopped pushing as soon as I saw that I was moving the center tube =) tried to push it back in place and it seemed ok. But when I've completely assembled the movement now I can see that when setting the time, the tubes around the chrono wheel can actually move a bit, they are not completely fixed, there is some slack in there, so to say.
Maybe this is due to the center tube not being pushed down all the way, so it can be fixed just by pusing it further down, or maybe I will need a new tube if it has come loose from its bottom plate. I will know when I disassemble the movement again, but I have to disassemble a lot before being able to replace the center tube, so I will prepare with a spare center tube in case it will be needed.