First of all, almost all phrasal verb + particle combinations can be used non-phrasally.
I kicked out my ex-wife = I compelled my ex-wife to leave.
I kicked out the wall = I kicked the wall which caused it to be removed partially or completely.
The meanings will depend on context.
Put on X means to wear X. This works if it's expressed as put X on.
Put in X for/on Y means to contribute X towards Y. Put X in Y doesn't usually mean this though.
So both your examples are not a phrasal put - it's just put being used normally.
That being said, you might what to know the difference between in and on. They don't mean anything substantially different in your examples and I'll explain.
X is in Y if it's surrounded on all sides by Y. This can be in a 3D sense where you are in a room or box, or a 2D sense where you are in an area or something delineated by lines, or even a 1D sense where a point is in a line defined by two other points. If Y is a container, something can be in Y.
X is on Y if it overlaps Y physically and Y is below/behind X. So you can sit on a chair, walk on the ground, etc. *On Y" is also used if we physically do something to the surface of Y, so you'll apply makeup on your lips, draw on the sidewalk using chalk, or paint on the side of a building.
So why can we say "in a commercial" or "on a commercial" and mean the same? It's because multiple models work with the concept of a commercial.
A commercial has "borders" - a start time and an end time, and various clips and such will make the commercial. So it's a container, and therefore content can be in it.
Is a commercial a "surface" things can be laid on? Yes - a creative person might think of a commercial as a blank slate or canvas on which things are placed.
So that's why in and on both work.