Drain clogged by grout
First I want to mention that your tile guy is 100% responsible for this.  He should be fixing this alone and paying for any plumbing issues.   This could end up being something that could cost you a few thousand dollars or more if you are in a city.  There is a chance that not only do you have grout (cement) blocking one section but it could be layering your whole line on the bottom.  Which you think might not be a huge issue if there is a 1/2 inch grout on a 4 inch pipe but this will build up constantly, especially if it isn't PVC.

There is very little you can do other than replace the pipes.  You can try liquid hammer.  My guys use this to clean their wheel barrows and tools from concrete and it really works.  However I am not sure it is suitable for pipes.  But really what do you have to lose?  I would contact the manufacturer of liquid hammer and ask them if you can pour it down a drain legally and what effect it will have on those pipes (my guess is your pipes will last).  Then pour if it is legal and see if first if your main clog is gone and then later if there are no issues with your main line.  Since it is your house you can monitor if the concrete is causing buildup on main line, and then repeat cleansing or having plumber come out with a bit to break it up.