We are not contractors but it sounds like it required 3 months for the new septic tank to fill up beforw it caused a problem. Which would lead one to question if the problem wan indeed the tank and not the leach field in the very beginning.
Our recommendation is to first collect information by speaking with the owners about the scope of work done. Copies of the paperwork and bill would be helpful before talking to the company that did the work.
This process should hopefully clearify what youn next course of action should be.