For an automatic update "feature" that has been spoken of so long time already, I think they should have gotten their PR/Marketing straight. "A few hours" usually means no more than 4, give them the benefit of the doubt and stretch that to 6 hours.

I received the message that 3.7.1 was available Wednesday morning, Oct. 30, 8am (GMT+8). Currently it is Thursday, October 31, almost 1am and none of my sites have miraculously auto-updated.

I'm sorry, but that is just poor PR

Then just don't give the update notice and when every site has been automagically updated after 3 weeks or however long they need, celebrate after the fact!