A fluorescent tube contains (when operating) a plasma, and this excites phosphors coated on the inside of the tube. Some of these phosphors are phosphorescent, that is they will glow in the dark for a while due to being exposed to light. But that glow will soon cease. Other phosphors are fluorescent, that is they will glow only while excited. So the glow you observe is due to the phosphorescent particles in the coating, and they will soon diminish in brightness.