Advice for finding someone to repair a plumbing problem?

it sounds like your toilet seal is leaking causing the water to come through the tile, you may have more floor damage than you think, you need to hire a licensed and bonded plumbing contractor who specializes in remodeling work. more than likely your floor will have to be removed down to the floor joists and a new floor installed. the toilet flange is probably cracked causing this leak so the contractor will have to remove this and install a new one along with everything else.