Ok here are 2 things that I did and they both worked:
If you have an area where you can go inside a place, then just keep going in and out of it. The gang will and should eventually show up.
If you are at an area where you can't go inside anywhere, then try this.
This one can be quick or time consuming. It all depends on where you are and I have had this trick work with both gangs, using both gangs.
Find a rival gang and start a fire or fist fight with as many as you can. Once you have started with enough of them start walking toward the are you need to take over (And they will follow you becuase you strted a fight with them) Lure them into the area. Then pull out you're gun and shoot one once to get them shooting at you.
Once you get 1, 2, or 3, of them shooting at you, just shoot them and that should trigger it. If this doesn't work the first couple of times keep trying. This is tricky to do.
NOTE: I have used the Yellow gang to trigger purple wars and used the purple gang to trigger yellow wars.
Now maybe this was a co-incidence that it got trigger by something else and not the other colored gang. But either way luring gang members to an are to start a war works. As I said already that, I had to do this more than 10 times while I was taking over territories.
Well I hope this helps people out.