Should a tenant be relocated while asbestos is removed from the ceiling?
"Asbestos in the ceiling' is rather vague. Are they referring to the ceiling itself? Popcorn texturing? Insulation above the ceiling? 

As for the danger level of asbestos, it all depends on if it is airborne or not. In its solid state, it's harmless. It's only when it's friable and turns to dust and you inhale it does it become dangerous. Even then, note that for it to cause cancer and the like, it takes a LOT of exposure and a LOT of time. Most people injured by asbestos were those that worked in asbestos plants and mines. So, while it is dangerous, there is no need to immediately panic when found in your house.

I'm going to assume the asbestos is part of the popcorn texturing. This wasn't uncommon and (AFAIK) the most common place to find asbestos in a lot of homes.

As long as no one touches it, it's fine. If it's painted, even better. Did the plumber expose a bit of the asbestos? Probably. Enough to be of any real danger? I highly doubt it. Enough to cause the insurer or city or code to force you to remove it? I have no clue. That's more of a policy/regulation issue.

If this is a rental, then removing will likely have to follow particular standards, and that usually involves a remediation crew that comes in, fully seals everything off, wets everything down, bags all the materials, vacuums with HEPA filters, and then carts it all off for you. Fairly safe, though potentially expensive.