Physics workflow of mantaflow has been tested, during years. But rendering of simulation with Cycles or EEVEE was not.
So, that is a known bug that has already been reported.
You can use several emitters of different colors with animated emission.
But blending of colors can not happen at proximity of emitter. It only occurs after a certain period according to blending of gases.
You can use color ramps in smoke shader. But they are relative to attributes of smoke, not to time.
So, currently, there is no solution in 2.82.
Smoke domain is supposed to become a Volume object in near future.
But it does not look like rendering of these Volume objects will be satisfying for that, in their early sate, too.
If color is your main concern, you should probably use a previous release.