Well, given the alternative was the destruction of our Galaxy...
Hate to tell it to you, but Voyager provoked them just as much as the Borg. Their first encounter with 8472 was them barging onto one of their ships as if they had every right to be there. Then they tried tractoring it, and beaming it away.
Their next encounter with Voyager, they're obviously collaborating with the enemy that invaded them. It's only then the "your galaxy will be purged" bit came. Which is a dubious and vague comment. Then they invade their realm... using weapons of mass destruction based on Borg technology. That's when they decided to target the Federation. And if they're all that evil, why was Janeway able to talk them down easy enough? They probably would've stopped at the Borg and gone back to swimming in their green goo absent Voyager.