The plumber should of ran the snake (was it the electric kind that has like a claw at the end or just the round skinny kind which will not do nothing down your main clean out, you might want to call the company that sent him and requst that they send someone else out, also could call your city water dept and let them know the your pipes are backing up and you have had plumbers out they have snaked you area and the clog is not on your side, I only recommend this because our city will do this,

If someone only charged that little I would honestly suspect he is NOT licensed plumber.

I would call the company back and tell them you still have the problem and to send a plumbing mechanic who knows to test their work prior to leaving a job site.

Considering the cost of tools and wear and tear and insurance and salary and the van /truck to get to the job site plus overhead and profit I cannot see how someone could travel to a home and charge so little.

Also the gentlem should have used 1/2" or a 3/4" wire snaking the main from the trap if there is one to street then inside the home NOT trying to snake from a sink trap.

Sounds like you have a main line blockage