Do you know why tubes are called valves? A plate on one side has a whole lot of electrons that are attracted to a plate on the other side. The signal we want to amplify is used to control another element in between that controls the flow of electrons. This is the "valve", and the small controlling signal compared to the large amount of current it controls is what produces the amplification.
Real basic stuff, which if you keep it all in mind then it is easy to understand what why vibration control affects tubes and why tube dampers suck the life out of the music.
In the process of electrons flowing across the tube all the different elements of the tube are vibrating. Always. Everything is. Not just the glass on the outside but the plates and pins and the amp or whatever the tube is plugged into.
All these parts, the glass, metal, all of it, each and every one has its own individual harmonic resonances. Just like a cantilever, speaker driver, anything you care to name. When they vibrate this changes the physical distance between tube elements, which has the effect of changing timing and frequency.
Think of Doppler. The car horn that is higher pitch moving towards you shifts lower when it is going away. Tube plates vibrating are sometimes moving towards each other shifting the sound higher, sometimes moving apart shifting it lower. This can happen randomly, in which case the tube will probably sound pretty good. Or the two sides can have resonant modes where the resonance of one aggravates or accentuates the other. This whole process is dynamic and can change with the frequency of the music signal. Or this same process might happen in a way that actually sounds pretty good. There is a lot of black magic going on in a tube.
What happens when you move the damper up and down the tube, you are putting mass and damping in different locations and this is changing the harmonic resonance characteristics of the whole tube system- not just the glass but all the stuff inside. Also since the tube is connected to the amp you are to an extent damping that as well. But just in the same way Pods under a component have more effect than under the rack, dampers on the tube affect the tube itself more than the amp. But make no mistake, it all goes together.
Dampers are known to suck life and dynamics, which is why hardly anyone uses them with anything any more. Springs and isolation are by far more effective, just hard to implement with tubes. Sometimes though a particular tube may have a really glaring hot spot resonance so bad it is worth the hit to everything else to tame it with a damper. This all perfectly explains what you did and heard.
Also explains why some find dampers worthwhile. It all depends on the situation and the listener. By and large though you will be better off to treat the problem at the source by isolating the whole component on springs.
