pj, what the store sold you was a man made wax-like product that is heavy in silicone. It's like Future floor wax. It can put a beautiful shine on but you will never be able to properly refinish the piece. Also, you shouldn't have to rub it to obtain a shine. It's kind of like those shoe polishing kits that have the same thing. The spray on shine is great until you wear the shoes and particularly in the rain. Other than that, they look great.
The wipe-down with naptha will be a big help! It will not remove the silicone. Nothing will, totally, and TSP is OK to use on unfinished wood but you are taking too much of a chance on finished wood to use TSP. Again, the naptha will be a help.
With that said, thanks for letting me know that you had used the silicon product. Since you already have silicone on the finish, you can use either Pledge or Johnson's Wax. I still prefer the paste wax and a tip for using that is to apply it to small areas. I don't apply it to more than a square foot or two at a time and never when the finish is already warm or in direct sunshine. When it just starts to haze, wipe it off.
You really might consider reading a book called Understanding Wood Finishing, by Bob Flexner. It's full of both good information about finishes and the real truth about many myths about various types of products for finishing and caring for wood. It's reasonably priced and available at most booksellers or your local library should have it. No, I have no financial interest in the book. It's very enjoyable and easy to read.