Caulk deteriorates naturally with high temperatures and intense sunlight. Both are factors when used on a roof. Better roof windows (Velux) are designed to need no caulk. The mounting systems use step flashing, top and bottom flashing and an aluminum cap that fits all around the window. You have to buy the flashing kits as an extra. This is just not an environment where caulk should be relied on to prevent leaks.
Almost all systems sold use a self-flashing or curb mounting system to deflect moisture. I am not aware of any product designed to be sealed with caulk.
Do you recall what brand of skylite or roof window you had installed? The place to start is with the manufacturers recommended installation method, and see if the contractor conformed. From what you have said so far, he sounds like more BS than know-how.