Hi, we need to see your scene to be able to help. For me, the light mixes correctly. I created a cube object, added a Volume material to the cube and included two spotlights - red and green. Everything worked as I would expect.
What you are doing is a bit hacky, but it still can be done. However, you have two volumes in one place where the lights intersect and that causes some troubles (I don't even know if that should work...). What you can do is put the cones into boole operator. See attached scene. It's a pity the boole operator only can merge two objects though :-(