As usual, the Lexicanum does an excellent job of summarizing things:
http://wh40k.lexicanum.com/wiki/Night_Lords#Descent
Just because I like hearing myself talk though, I'll give my own shortened version. The Night Lords went rogue shortly before the Heresy started. Konrad Curze was supposed to stand trial (more or less) for the Night Lords excessively brutal tactics against Imperial citizens, and for savagely attacking Rogal Dorn when Dorn confronted him about this.
However, even though Curze let himself be taken prisoner willingly, he decided he didn't want any more judging at the hands of the other primarchs, escaped (killing a bunch of IF and
EC along the way), and returned to Nostramo, where he ordered his legion to destroy the planet as punishment for falling back into crime and corruption.
The Heresy started soon after, and Curze was quite willing to betray his brothers at Istvaan V.
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As to why the Night Lords were even trusted at all to stay loyal at Istvaan V, who knows. I'd like to see any sources that seek to explain this. Personally I feel Curze was always so crazy that even beating up Dorn and destroying Nostramo weren't seen as signs of rebellion, just Curze being Curze. He'd otherwise been loyal to a fault, doing exactly as told as best he knew how (instilling fear to maintain Imperial control), even when everyone seemed to hate him for it. Bringing wayward legions back in line would sort of fit the Night Lords usual role of scaring rebellious planets straight, so while I imagine Dorn would have some complaints, the other primarchs were probably glad to have the crazy-scary one on their side (or so they thought).