You should find this step-by-step guide useful: How To Repair Cracks In Plaster. You shouldn't expect to see any lines, cracks or distortions once the plaster repair has been completed and the area painted. - MitchellMc
You can repair this yourself if you have the proper tools:
A ladder to reach the ceiling
Plastic plaster joint knife (to spread the plaster)
Polyfilla for easy fix of cracks
Sanding block to finish or sanding pole
Set ladder and make sure it is stable
Go up with Polyfilla and joint knife and start filling the crack
Wait for drying time
Sand to finish. You may use a sanding pole for easier use.
I have found that hairline cracks aren't possible to fill because not enough filler can get in, so you end up with a super thin coating over the top that falls off like dust when dry. The best way I have found is to run the sharp corner of a scraper along the crack to make it a V shaped crack. Then it has depth and enough surface area for the filler to properly adhere to. Then fill that crack and sand it flat when dry.
I would imagine that putting tape over the crack would then introduce 2 more fine lines at each side of the tape that would need to be covered. Then he would have to add a coating over the tape to hide those tape edges, which would result in a mound on your flat ceiling. This could be blended in by making it wider, but it seems like it would add more problems than it solves. The thing with ceilings is that bright light often shines across them, so any variations in thickness looks worse than it does on a wall, where the light usually arrives from many angles. (Try shining a torch along a plaster wall to see how (un)flat they are.) If the 2 edges of adjoining plaster sheets are attached closely where there is timber above the join, the tape shouldn't be needed. It may be a case of redoing the fine cracks once more now the plaster sheets have settled. - TedBear