I have 2 requests I made this weekend and the other member says they mailed the book on Sunday. Really?

If they did printable postage, and dropped in the drop box at the post office, I would consider it mailed, even on Sunday.

Also, some p.o.'s are open on Sunday (though very few).

I mail a lot of books/packages on Sunday. With all of the kiosks and sub-stations you can buy postage like many Hallmark stores, gas stations and hardware stores near me that are make shift post offices, there are plenty of places to do this. 

I often mail with stamps and the moment I have dropped it into a big blue box, I mark it mailed, and that is often on a Sunday, even tho it might not be picked up until Monday afternoon. The moment it leaves my hands I mark it mailed.

Just a wild guess:  They could have mailed the book(s) on Saturday and were unable to get to a computer until Sunday.