Great, now I'm confused. There's no way that my original belief in the childhood friend and informant being the same person could seem reasonable now that they (apparently) reacted to the news of his success in different places but the same time; however, someone here in the comments is still convinced that it's still a case of split/dual personality, and I wish I could share that sentiment, but I'd need to understand his reasoning first...
This was first hinted at/foreshadowed when Kaede's shapeshifting/illusion magic was revealed; the same chapter Mae is introduced. Further credence is lent to this theory when the MC notices that the markings on the talismans he receives from Mae are the same ones used by Kaede's family. Finally, it is also strange that Kaede and Mae visit him back-to-back, almost immediately one after the other. With how possessive/closely Kaede watches him, I find it unlikely she wouldn't have noticed (and taken issue with) the cute kouhai with big boobs nuzzling up to him on occasion (unless the two are one and the same).
I suppose it is possible that Kaede could be unconsciously transforming into Mae as a way to express her true feelings towards Furuya. Think dual/spilt personality disorder, which wouldn't be too farfetched given the huge amount of pressure she probably lives under as the next head of a prestigious family. That and the mention of possession in this chapter has got me thinking it could be a familiar/spirit/apparition.
As for the differing reactions, that could be down to the context of each conversation; Kaede talking to another exorcist, while Mae is talking to Furuya on the phone and being thanked by him.