I used the ballast from a 5w cfl, and even in the difference of 1 watt and being run for only a few moments, my F4T5 got a noticeable end darkening. But when I run other size of fluorescent lamps on higher wattage ballasts, they don't care much. The filaments on a cfl are smaller than a T5, so why is this happening?

Dunno the exact specs of the cfl, but very often ghey are designed to operate at significantly lower currents (so higher arc voltages), in order to cut some of the cathode fall losses off. So the F4T5 could well be significantly underdriven (the ballast is very close to a constant current source), so suffering from cathode sputtering.

Or it also possible there is nothing wrong with the setup, the observed blackening is just a condensed mercury. If this would be the case, the "blackening" should disappear once the lamp warms up completely (after about half a hour running) and appear back only when the lamp cools down (so few minutes after power down) or even only at the next stsrtup.

Seems like mercury condensation and the arc stabilising, after a few minutes it looked okay with my white one. But my F4T5 blb still has slight banding from it.

Update- actually, I think it isn't mercury. The lamp end got a slight teardrop shape. This lamp also seems to have a loose connection, so maybe the cfl ballast is striking it on hot cathode, but the arc remains when the lamp is in cold cathode mode (lamp is shaken and connection loosens). But I don't think this is the case, because my other lamp is also experiencing this on this ballast.
Also, in the picture, the spot isn't the filament structure, as it wasn't there before I lit it on this ballast. The lamp hasn't been running on it for more than 15 seconds.