Remember that first chapter when Fujimoto gave Rin the mobile phone and told him there was only one number in it, that it was the number of a friend who would help him?
And then, after the funeral, Rin rings the number and Mephisto pops up and we all assume he was the friend Fujimoto was speaking about. But, in truth, none ever answered Rin's call.
So, I was thinking, what if it wasn't Mephisto's number in the phone? Sure he popped up right after Rin ringed and he was holding his mobile to his ear (if memory doesn't fail me) but so what? He is the freaking King of Time and Space and can freaking be in two places at the same time and not be seen if he doesn't want to, plus, there had been a funeral, so Fujimoto's death had already been reported so he knew Rin or Yukio would eventually have to go to him since he was the only other person who knew the secret.
Ok, I know what you are thinking, whose number could it have been if not Mephisto's?
I have come up with 3 options:
1 - Shura, she knew Yukio, and Fujimoto had already manifested his desire of her being the one to teach Rin how to handle Kurikara. Problem with this theory: Fujimoto and Shura weren't in talking terms so we don't know if he kept going with that plan after she refused.
2 - Tatsuma Suguro, he was really comprehensive about Rin being Satan's son (aka, he didn't give a shit and invited him to chop watermelon and talk about Bon being a jerk), he already knew Fujimoto and has knowledge of Kurikara.
3 - Someone we don't know (yet) and who never got to know of Fujimoto's will to have him take care of Rin and Yukio.
I mean, I have a hard time seeing Mephisto as a villain if Fujimoto deemed him a friend so I thought this.
Onto how Mephisto got the call instead of the intended person:
A) He changed the number in Fujimoto's phone to his own.
B) Killed the person intended to get the call (in option's 3 case) and took the phone.
C) Since Rin never gets to actually speak on the phone, maybe Mephisto was monitoring the line/was watching hiding somewhere and when he saw Rin dial the number he just appeared before the intended person answered the phone so Rin just hanged before the person answered.