The blue was always running into the red, we call that "Bleeding" as the colors run into each other like that :) His first picture, he's stressed and so he's dull looking and not very bright. As he settled into his home, his real colors come out and brighten up as you see in the last picture. So the color hasn't actually changed, yet, but just brightened up is all. Eventually, yes, the blue will take over the white on his fins and likely his body as well, though that could possibly stay that Grizzled pattern. So, he'll eventually not be a Butterfly but a Multicolor; those who do not have a definite pattern or color type.
And yes, Double Tail refers to his tail type as does the others like Veil, Halfmoon, Crowntail, Plakat, like those. Colorations is a huge category but some typical ones you'll see are Solid (Red, Blue, Yellow, Black, etc.), Butterfly, Marble, Cambodian, Mustard Gas, etc.
Wilds: Wajok, Rutilans, Siamentorialis, Hendra
Leopards: Luna, Astrael, Dorian, Cullen, Gallifrey
African Fat Tails: Nox and Lux
Bearded Dragon: Stormfly