Red Thirst was starting to appear more and more during the Great Crusade, Black Rage is the psychic echo of Sanguinius' death at the hands of Horus.
Red Thirst is a bloodlust that comes upon them during battle, marines with exceptional willpower are usually able to suppress it, which is why marines like Dante are rarely if ever seen in this state.
The Black Rage is far more unpredictable, they don't really know what brings it on and although Astorath seems to be able to tell who will fall next, they have little to no warning. Eventually, even Dante himself will fall to the Black Rage if he doesn't fall in battle first.
I've suspected for a while now that the curses have nothing to do with gene-seed and everything to do with the fact that their Aspirants drink a tiny portion of Sanguinius' blood to initiate the change into Astartes. His blood itself is psychically charged, and this could account for the Black Rage. Also, the Red Thirst may have been a mutation in Sanguinius himself from his time spent in the warp that he passes on through his blood. The original Blood Angels were made through traditional gene-seed methods before Sanguinius was found, and so they were clean. As the Great Crusade continued more and more of the legion's ranks were filled by those who underwent the blood drinking ceremony and consequently the cases of Red Thirst went up. Obviously this is all speculation on my part, but that's my take on the subject.
EDIT: Tycho's death was tragic, but that is what makes it great in my opinion. I tip my hat to Lynata for directing me to
this incredible short story regarding his death, which I now in turn direct you to.