Mine have always called my mom Ms. XXXXXX. Unless I marry them, I'd be miffed if they thought they could start calling her by her first name. It's rude and overly familiar for my tastes. (One ex called my mom by her first name in conversation with me and I promptly told him that we weren't engaged so he needed to refer to her as Ms. XXXXXX.)
Of course, I'm the sort of person that anytime an adult said to just call them by their first name as a child I never did it - it creeped me out that an adult wanted me to address them they same way I would a peer. I either felt that they were facetiously trying to gain my trust (like a school counselor) or they were just...creepy. I was raised to call my elders Mr/Mrs/Ms so that's what I did.
(Of course, I had an ex that said I should call his mom by her first name, but she never told me that herself. Apparently that was one reason she never liked me - because I called her Ms. XXXXXXX - even though she never said ANYTHING to me about it. That family was so messed up though, I was so grateful to escape in a lot of ways.)
Now that I'm almost 30, I've just now started calling some family friends by their first name - it started out as being mostly for my mom's benefit as she didn't always remember their last names right after her surgery.