To the OP:
14 CFR 61.129 "aeronautical experience" spells out the requirements. Note the places where it says "in an airplane".

If your school has an FAA-approved Part 141 training course outline for a helo-to-fixed transition course, then that will override 61.129. If, on the other hand, the school just has a typical Part 141 Commercial TCO (for normal fixed-wing Private pilots to follow), that will include more hours than you need. If they expect you to do their full "normal" Commercial TCO, then it will be long and expensive. You, or they, may just elect to train you to meet 61.129.

Is that clear as mud?