Were Westinghouse's Chinese HID bulbs made in China by Philips or at a separate factory?

They were completely separate, however there was some modern Westinghouse HPS lamps manufactured by Philips at Bath, NY.

Most modern lamps made from the big three are outsourced from a different manufacturer now. For example, GE is now faux GE, Sylvania is now faux Sylvania. Philips May still make some lamps. I don’t think GE even makes their fluorescents in the US anymore, their modern ones, even the ones made in the USA, with the trash can symbol on them, were very prone to mercury starvation and going pink. GE really reduced the quality of their fluorescents before discontinuing them, and GE only started adding the “CONTAINS MERCURY” and no trash can on their bulbs in 2020 when Savant bought them.

I’ve seen a few mercury starved GE F40T12 too, tho not as much. I believe GE closed this U.S. fluorescent lamp plant in 2023. GE and Sylvania have now unfortunately faced the same fate as Westinghouse. They use the big name but I notice that in GE and Sylvania now, all I see is the logo, like “GE’s best incandescent line” was replaced with “Our best incandescent line”. Faux GE light bulbs are junk.

Not sure how good the GE mercury vapor lamps are but all mercury vapor lamps tend to last a while. Their modern MH lamps are generic, tho they used to be pretty decent.
Philips, is the only manufacturer that still makes some products,  I believe Philips still makes incandescent bulbs, fluorescent, and LED. Signify is just a rebrander, not a buyout. Everything from GE and Sylvania now outsourced, but GE’s snow cone LEDs with the 15,000 hour lifespan are pretty good bulbs. The only decent thing GE can make is their mid-range snow cone LEDs, their low end 7500 hour ones with the black insulators are junk. Those are rated at 7500 hours for a reason!

The new 3500 hour GE LEDs are less efficient and only have the life of a 130V A19 incandescent so wouldn’t recommend those LEDs either.

Yeah I think Philips (Signify) is the only one of the big three that still makes some of their lamps, I believe the T8 and T12 fluorescents they still make. Interestingly, I think GE (Savant) has been sourcing F40T12 lamps and possibly other fluorescent types from Signify after they closed the Bucyrus, OH lamp plant in 2023. Two changes happened at the time, they started being sourced from India which is where Signify makes their F40T12 lamps and the lamp specs were subtly changed to match the Signify specs, GE's 4100K F40T12 used to be rated 2900 lumens, which changed to 2600 lumens to match Signify's.

With GE even back in the 2000s, one telltale way to identify a outsourced lamp was to look at the back of the packaging. GE produced lamps would say "Made by GE" while outsourced lamps and fixtures would say "Made for GE". I remember the linear fluorescent lamps would typically say "Made By GE" while imported lamps such as the self ballasted CFLs would say "Made For GE".   

Actually, Sylvania still makes some of their products in-house. Though tubes like F20T12 and F15T8 are made by Opple...

I think they still make their PL9/13 bulbs on the same equipment that the original Maybrook, NY-made CFLs were made on... 5 and 7w appear to be outsourced to Opple, however.

It appears to me that Sylvania makes their A19s at one of their own plants in China, though I wouldn't be too surprised if some of their stuff is sourced from Foshan or K-Lite. @James , can you corroborate or disprove this?

Westinghouse lamps made in China are relatively modern things, and have no relation whatsoever to either Westinghouse or Philips / Signify.  They are sourced from a large number of different Chinese companies who stamp the Westinghouse name on their products, under license from Angelo Brothers of USA which bought the rights to use that obsolete brand on its lighting products.

As far as I know GE/Current/Savant and Osram/Ledvance/Sylvania have shut down all of their general lighting plants worldwide.  Philips/Signify not quite, it still has some small remaining operations of its own in Poland, Belgium, India, China and possibly also Indonesia and Thailand.  Some of the factories and machines formerly built by these companies have indeed been sold on to other third parties and are still in production, and a few of those do still produce under private brands for their former owners.

@James – What about Ledvance Russia?