Alien aggression is a global affair, at least to an extent. You can tick off specific aliens by getting close to their nests, but otherwise, the level of alien aggression is something that affects all nations. If one person goes after aliens too violently, all aliens are going to respond. This can be useful to you in specific circumstances.
If you have a good military and other people are lacking in that area, you can use the aliens to do some of your dirty work. Attack the aliens until their icons turn orange (and eventually red), and watch your borders carefully. Fight off the aliens that come calling, and know that your rivals are going to have the same problems with them. Because you have a stronger military, this is less of a threat to your people and more of a threat to your opponents.
Note that you won't make friends with more than half of the nations when you do this. It's more of a warmonger's strategy than something everyone should try. Nations that are trying to live in peace with the aliens are going to get annoyed. Don't make promises not to attack the aliens, or they'll get even angrier when you keep doing it.
Now, it's unlikely that the aliens are going to kill your opponents outright. That's not the point. Instead, you're hoping to force others to defend what they have, put more Production into defense, and delay their development in other areas. If not, they'll lose outposts and scouting troops far more frequently.