Again, I am not an expert, but offhand I can't think of any illness that would cause it. If he were irritated at all, he would be closing his fins tightly against his body.
My personal guess is that now you are taking care of him, he is healthy and changing colors. There was an example of someone's betta completely changing to another color on here. The type of blue is a color commonly seen (and which I think is beautiful) on bettas - so it isn't a surprise that your other betta has some of the same color. I would watch and see what he turns out like.