Update: (and many thanks for your replies!)
They haven't moved to the new formicarium and are using it as an outworld and dump site, and still prefer to live in the syringe. Well, if that's what they want...
I've started to feed some water into the syringe from the entrance where one fits the needle in. I only give them 1 or 2 ml of water, as the cotton will easily spill out and flood their chamber. They freak out from the vibrations and I believe they sense the imminent danger of flooding, but quickly calm down and go back to business.
Yes it seems Messors can be quite stubborn...
I have another colony that is also inside a syringe, this one completely dried out but they keep on living there.
The syringe is inside a plastic pen case that also has a test tube with water but they never moved there, every once in a while they go there for a sip of water, queen included. I guess the closed case (with a few tiny holes for ventilation) keep the inside of the syringe moist enough for her brood. I think these colonies aren't developing as fast as I expected. Lots of larvae and pupae and they seem about to explode, but I think they're taking a longer time to develop.
Fun story: Once the queen decided to move her eggs into the test tube. She brought the eggs in and immediately a worker would grab them and take them out back into the syringe! They went back and forward quite a few times, crossing each other but never realizing they were undoing the other's work! I've watched this for a good 5 minutes until I went away and they kept doing it... Too bad the plastic case is a bit opaque for a good filming, this would make a hilarious video!
And regarding the queen doing all the work, when I feed the several colonies of Messors I have on the test tube, they freak out due to the vibration, panic sets in, some workers come to inspect the dead insect and can give it a couple of bites, but generally it is the queen who comes out with freaking open jaws, goes around the insect and then head backs to check on the brood and does this for a couple of times, and later when she's feeling calm she comes back, starts biting and chewing on the insect and then drags it back into the pile of larvae for feeding.
Also, most if not all my Messors enjoy sugar water every once in a while. And it is the queen who usually goes there first and stays there drinking for half an hour or more, returning to her brood (to check them out?) for some seconds and then returning back again for some more drinking.