The company has a reason to be called Roto-Rooter. If you have a leak, the tree roots will find it and will fill the pipe with fine little roots that will plug the pipe. I cleaned out a drain pipe (not sewer) that had 6 ft of matted fine roots filling 2/3 of a 4-inch pipe.
You could have dampness under the floor without a leak. It can seep in from the edge of the foundation, or can percolate up from groundwater. That is why there is often a vapor barrier under the concrete.
You might deal with future growth of existing roots by trenching outside your foundation. Dig down below the footing level, and cut off any roots that are going under the foundation. AFTER you cut them off, you could apply a very strong dose of Round-Up and/or 2-4-D to the fine root system under your floor to try to kill anything that is already there. If you put some down the drain it might kill any roots that are already in your pipe. I'm not sure the Round-Up or 2-4-D will work but I believe in the Shock and Awe principle of attack.