Short answer: No, they use underwater lamps with normal light (maybe more intense light than a normal underwater lighting device) and coloured filters for the lens.
Note that I said "coloured filters" without saying what colour the filter should be. This is because the colour of the filter one would use for underwater photography depends on the depth you are at the moment you take the picture (and of course the direction you are keeping the lens. If shooting upwards you will have other lighting conditions compared to shooting straight ahead or downwards).
The deeper you go under water, the more the light would be filtered by the water. It's a gradual process.
Quoting from Underwater Photography Guide:
At what depth underwater does color disappear?
Red - 15ft
orange - 25ft
Yellow - 35-45ft
Green - 70-75ft
I would recommend reading some guides on Underwater photography or even taking a class. PADI, at least, has special classes for underwater photo and video.