You really can't say this is how it should look everytime. Typically a DBT is a protection tool.
If a unit has a major fault (short) the unit acts like a light switch. Bulb at or near full brilliance instantly and stays there. If a unit has this condition its fuse will blow (hopefully) but leave you no powered testing options.
Ideally (with the proper sized lamp (lamps), at power on bulbs should be bright (brighter) instantly then dim until faintly lit (possibly dark, depending on unit , lamp size, overall brightness in room).
You are in essence creating a voltage divider network. 2 series impedance loads. The bulb mostly a fixed value (I'm sure its resistance (impedance) changes as the filament heats but for sake of simplicity we can call it a resistor. The unit normally would have a low resistance (impedance) at instantaneous power on, then as PS caps charge its resistance rises (caps become charged and it becomes less conductive. )
While it less than perfect, the bulb gives you a visual picture that the unit is powering normally. As a testing tool (this is less precise, because certain tubes must reach a certain temp to conduct but)
You can measure actual v in to unit and with some degree of accuracy test for percentages of voltages that should be present at certain points without risking releasing magic smoke.
To a degree with multiple lamp sizes (or possibly multiple bulbs you can adjust the voltage at the unit by varying bulb size (sort of a poor man's variac.
(Under some conditions its advantageous to run variac through DBT to unit)
Its also useful (to a degree) starting old gear. It gives the electrolytic caps a chance to reform.
Clear as mud right?
Seriously, if something isn t clear, ask.