I think it was made for his company, note the engraving on the winding bridge. Much the same as the BB&B on Geoff's watch.
Yes, these were exactly the things I noticed that made me unsure. To complicate things, I believe that A. Newsalt was not only his name, but also the name of his business. It might be difficult to have certainty, but I'm not sure it's necessarily so important.
OK, here is something maybe interesting. This lot at Christies (sorry I haven't figured out how to get movement photos) says the following: "case, dial, and movement signed by maker, movement signed by retailer" And it obviously seems like a ladies' piece. https://www.christies.com/lotfinder...very-fine-and-attractive-5759160-details.aspx
Another ladies' PP, where the listing says "retailed by A. Newsalt". Can't find photos of the movement unfortunately. https://catalog.antiquorum.swiss/en/lots/patek-philippe-lot-144-204
OK, I've found more of these, but one good example here, similar to @verithingeoff's in a way. Based on the number of these that are turning up, it seems likely that the engraving indicates that they were made to be sold by A. Newsalt company. This was sold in 2014 for 2,750 GBP. "The dial signed Patek Philippe & Cie, Geneva, Switzerland, the movement signed Patek Philippe & Cie, Geneva, Switzerland, A. Newsalt. Dayton. O., 18 jewels 8 adjustments, No.160811" https://www.christies.com/lotfinder/Lot/a-gold-openface-pocket-watch-by-patek-5772856-details.aspx
