The typings aren't grouped solely based on the characters attributes. Yes, that means some characters get shafted because they get a bad typing, but it also lets you have things like a Power character that isn't SLLLLLLOOOOOOOOWWWWWWWW.
So no, not every buff character with a big weapon is automatically Power, not every fast character is automatically Speed etc.
I swear they just used a dart board to choose who gets what. Especially the characters who got moved into Technique when the typing does them little to no favors, especially since they removed the ability to EX any charge from Tech.