Do tourists with 10 year 60 day visas need to check in with the PSB whenever they reenter China?

Yes! Theoretically within 24 hours, and I always do it, although if it's on a weekend I find that the person in charge of registering me is not working until Monday morning. So I point out to them that, well, here I am today, see you again Monday (and at my PSB paichusuo it's all relaxed and friendly). But if, somewhere down the road, it is decided that lazy law-breaking 'tourist' foreigners are a problem I don't want to get jumped on as part of some category that 'they' do not like or whom they have lost patience with.

Alien, I agree the process is painless. Never had a problem showing up on Monday or even a day or two late.

In fact, the ladies that do the registration get to know you so it is all smiles, then you wait a few minutes. Then they give you your passport and the Registration Voucher and you say 好好，好的, with profuse 谢谢谢谢,再见,再见! A big smile helps too.

Seems a bit odd since I doubt that most "real" tourists coming to China have never heard of the PSB and often land wherever in China and then proceed to go on tours. I don't recall the customs people telling me to register (and most foreigners can't speak Chinese and probably couldn't find a PSB office

If you are staying in a hotel, they will do it for you. If you are staying with friends they will need to help you.
Air b'n'b seems to be a grey area, and there was a big news story on Kunming/Yunnan TV last week about unregistered visitors/tenants (Chinese nationals) in Dianchi Weichen area, and so I expect a clampdown on Air b'n'b type services in China as well as other countries now doing it.

As far as I know you only have to register at the local police bureau. That is if you not staying at a hotel or guesthouse that does the registration for you.

surprised they don't just attach a tracking device onto my passport. save me a trip, smirk

thats what mobile phones are for

why would they track your passport when they have facial recognition to track you.

I am from BJ. My flatmate was a non-Chinese. In July around less than one month before his work visa was expired, a policeman called. He also asked me to register telling that non-locals should do it if the stay was over 3 months in KM. In the evening two policemen came and photoed our documents with a special APP in the phone.