We are expected to adapt to their way of doing things, yet they make no such adaptations? Not that asking to be paid on time is even an adaptation really.

Unfortunately, late pay can be the stark reality in China. As for complaining, it's quite possible that will result in a dastardly reaction from your employer - it's all too easy for him to get his own back by resorting to fault finding with your teaching when there isn't really a problem with it. It would be easy enough for him to fabricate that some students are dissatisfied with the quality of your teaching in order for him to get his revenge.
I have rather a lot of foreign currency in a bank account here, to be used in case of emergencies that may arise. I can use some of it to keep me going in case of late payment, no problem. That does not mean I won't complain if need be, but only if I find myself compromised by my employer's non-obeyance of my contract. I can assure you that I'm not another paper tiger of a foreign teacher in China, unlike many foreign teachers I've come across here who are absolute crawlers - I have caused my Chinese employers big problems in the past, and have made them lose face bigtime as and when necessary. I'm like a coiled snake, ready to strike at a moment's notice, and being sent to Coventry doesn't bother me in the slightest! I don't need their pretence of friendship.