Okay, so here's the skinny.
1. The Evucks have to be on a gas giant, as you know.
2. At least 4 hours of "game time" have to have passed. That's not how long you have to play, because that includes the sped-up time from fast forwarding during dispatches, etc. Generally speaking, I believe it's 9 years per hour of game time, so that's 36 years in you have to get, roughly. If you hit escape, you can see the game time in the menu there, as well as the actual literal real time played.
3. The Evucks have to only have one planet remaining in their possession.
4. The Evucks have to be under attack from a "far superior foe." This requires that:
a. Some other race is attacking the Evucks.
b. The Evucks have fewer than 5 armadas, while the other side has more than 40.
c. The total armada power of the Evucks is less than 20x their power.
The logic on #4 might need some tweaking, now that I look at it.