The sewage accumulates in a covered pit, probably in the basement, and when it gets high enough in the pit, the pump turns on and moves it out high enough to flow down into the sewer by the street. The clunk you hear may be a check valve (a one-way valve to prevent what you pumped out from falling back into the pit in the house). If the check valve is not doing its job, sewage from the street could possibly back up into the house and then up into your fixtures from their drains. Normally, this should not happen, since the sewer should not be under pressure at the street, and the check valve normally prevents stuff from getting back into the house anyways.
But, if the line is plugged, weird things can happen.
There should be enough slope in the line going from the house to the street so that once stuff is pumped up and out, it should flow by gravity to the street and into the main sewer line. If that line is not installed properly and slopes back to the house, the only thing preventing stuff from backing up into the house is the check valve.
Also note, draino and other drain cleaners will not help with most types of clogs, and can accumulate and mess up your pipes, pump, and fittings. It might help with a small hair clog or grease clog, but even then, should not be your first response. It can ruin a pro's tools and cause burns. You need to tell them if you've used it recently so that they can take precautions.
Has there been a lot of rain recently? Some towns have what are called combined rain/sewer lines. The EPA is trying to get towns to separate them. If you have a heavy rainstorm, it can overtax the sewer system and put sewage in places it shouldn't be, like your tub.
My guess is that you have a clog, and need to get the sewer line cleaned. Sewage backing up into the house is neither normal nor healthy. Depending on what they find, if it is roots, or something else will indicate what else, if anything needs to be done.
If this has to be repeated because it comes back again, I'd consider having them put a camera down there and scope it out. It might reveal a damaged line or the source of the problem. You might need to take the check valve out, clean it up or replace it.