It is not about voltage between one and second filament when the starter switch is OFF, but about voltage between filaments and the external (grounded) metal work, when the starter switch is still ON

During the preheat (starter switch is ON), both ends are on the same potential, as they are shorted together by the starting switch.
Assume the metal part close to the lamp is grounded.

So if the lamp is on the neural side, the filaments are on the neutral potential during the preheat. So there is no voltage between the electrodes and the metal outside the tube, so only electrodes get heated during the preheat. So only when the starter switch open, the voltage between tube ends start to develop a ionisation.

But when the lamp is on the phase side, both filaments are on the phase potential, what mean you have the mains voltage between filaments and the external metal parts. This form a discharge with one direct inner electrode (filaments) and one capacitive coupled outer electrode (the grounded fixture metal body/reflector/...)
This discharge is nearly not visible (maybe in the dark as tiny glow progressing from tube ends; this effect become quite bright on HF), but as it is ionisation at the end, so when the starter switch open, there are already many ions present to start an avalanche into full arc between both tube ends.