This question would be greatly helped by actual examples. It is difficult to come up with a realistic scenario where "put on a commercial" would arise.
They put his endorsement in the commercial
They added his endorsement to the content of the commercial.
Nor is "put his endorsement in a commercial" include the phrasal verb "put in." The verb is simply "put."
There is a phrasal verb of "put on" that means to "present," particularly in the context of presenting a play on stage.
They put on "Much Ado About Nothing"
They presented the play called "Much Ado About Nothing."
I have never seen that usage with reference to a commercial, but I suppose it's remotely possible.
Of course, "put" is also a stand-alone verb that can take various prepositions, including "on."
They put the commercial on television
does not involve a phrasal verb and means
They displayed the commercial using the medium of television.