I think you need to stop talking as if the heater is a tube is a seperate element when they are not..
A fluorescent lamp consists of a glass tube, filled with argon gas, and dosed with a small drop of mercury. At each end there is a cathode, which are normally made of tungsten, because of its low evaporation rate. The glass tube is coated on the inside with a layer of phosphors.
When a fluorescent lamp is turned on, the current heats the cathodes at each end of the lamp, causing them to emit electrons. A stream of electrons flows through the gas from one electrode to the other. These electrons bump into the mercury atoms and excite them. As the mercury atoms move from the excited state back to the unexcited state, they give off ultraviolet photons. These photons hit the phosphor coating the inside of the fluorescent tube, and this phosphor creates visible light. Reducing the current across the cathode will reduce the electron flow from it, and thus the amount of ultrviolet photons produced, and this in turn will reduce the amount of visble light emitted by the lamp.
In summary:
There is a stream of electrons flowing between the electrodes at both ends of the fluorescent bulb.
The electrons interact with mercury vapor atoms floating inside the tube
The mercury atoms become excited, and then when they return to an unexcited state they release photons of light in the ultraviolet region of the spectrum
These ultraviolet photons collide with the phosphor coating the inside of the bulb and the phosphor creates visible light.
The amount of electrons flowing in the tube id directly proportional to the current flowing across the cathode at any one time.