and make it weird that TER would let BP advertize on here too.

Both City Vibe and Back page are sponsors here on TER.  In other words they pay for ad space.  City vibe ads also link to TER reviews if a provider has any.  Back page also winds up with content from Cityvibe and, from what I have observed, Eros, in the form of provider ads.

Does this status as an advertiser on TER make either of these sites more reliable? No.  Cityvibe and BP are both ad sites. Anyone with the necessary funds can place an ad. How reliable that ad may be, as always, is unclear without reviews to rely on for verification.  TER does not administer CV or BP and there is no reason why you should read an ad on any ad site with anything less than total scepticism. CV and BP both also have a habit of leaving ads up for weeks months or even years after they are placed which means that a lot of these women are not even available any longer.  My former agency ATF retired three years ago and there is still an ad for her on Back Page which, by the way, her former agency didn't even place...it was lifted from an Eros ad.

It's always buyer beware unless you see actual current reviews.

I assume it is run by / somehow connected to TER.  Does this mean it is more reliable than BP?

You need to research the lady, meaning find reviews, and remember, TER is not the only review site.
While I am not allowed to mention other sites, there are regional review sites and other national sites.

And you picked the right place to ask it.

...I've seen CityVibe ads that appear to have been somehow auto-generated from TER reviews. That is, I've reviewed an escort here and soon afterwards, a CityVibe ad will appear that that includes text and photos from a much earlier BP ad listed in her profile. I've seen the same apparent pattern when I've googled the phone numbers of other escorts I'm checking out.

(Pardon me if all this is common knowledge.)

In the world of the internet there is a lot of data sharing (sanctioned or not) that goes on between websites.  
It doesn't necessarily suggest anything. Some site send bots out to skim data from other sites, some sites offer data sharing APIs, could be any number of causes for patterns like that to develop.

REAsearch.............................Research....................its good for confidence and reference for reality

RS2k promotes itself primarily as a client verification service, but it also carries a good number of ads.  The site purports to requires advertisers to provide verification as well.  Does that make RS2k advertisers reliable?

I cannot speak to RS2k, as I use p411 - but I can say that I have found some unreliable ladies on p411, so I am not sure how much screening, if any, is done by those sites. It would be nice to be able to provide OK's for providers in those site - not necessarily reviews, but just some simple data - YES, she is real; YES, her pics are accurate; and maybe YES/NO for recommendation.