It was implied that Mikael turned first, then his children, although not explicitly shown.
All we see is that Rebekah fed and presumably turned before Klaus, with the remaining siblings' order unknown.
However, given Mikael's attitudes he probably saw to it that his real sons: Finn, Elijah and Kol turned first. And then he went to Rebekah and Klaus, in that order because even even though she may be a 'lowly' woman, she was at least his daughter. Klaus was probably the last to turn.
Indeed, you are correct. I did remember the order incorrectly. (Though it would explain things if Mikael had had suspicions but no proof, as above.)
For whatever reason, Mikael had such a intense disdain for Klaus that he grouped him with Rebekah, who we saw feed first.
Depending on whose story you believe (Elijah & Rebekah) one of them claimed that Mikael already knew Klaus wasn't his but didn't know he was a werewolf until his first kill. Then there's the one that says Mikael didn't know that Klaus wasn't his until his first kill.