Every year they do that to check on everybody not just foreigners. They want to check if there are any criminals living in the complexes. That is what my wife told me. We had to do it to about a month ago.

The people who do the registration are invariably friendly and you won't get into trouble even if you register very (weeks) late.

I think cloudtrapezer is generally right about registering weeks late, but I don't think anybody should take it as guaranteed - I remember a particular weirdness that happened to a friend, although it was over 10 years ago.

However, on Sunday I arrived in Kunming late, coming from abroad; law says I have to register within 24 hours; I went to the PSB 48 hours later, and because of National Day/week, the person who registers (foreigners, at least) wasn't on duty. The cop on duty there checked with somebody upstairs, then told me to come back early on Sep. 8. I plan to do so, but you can see that it's (often, I believe) somewhat loose.
Have never had the slightest trouble or aggro at my local PSB office, over many years and with various types of visa. Maybe once a year (actually it seems much less often) a cop does visit my flat, look at my passport and then leaves, no hassle.