I do a lot of low water immersion dyeing,
the colors always end up a little muddy, so it's best to start with pure colors and let the secondary mixes happen naturally when two colors mix.
From the way I understand the fiber reactive dyes to work, heat is not going to help the turquoise dye if it's before the soda ash is added.
My method for LWI is to prewash, and then soak the fabric and then I'll either go one or two routes, one is cram the fabric into a container and then pour the dyes over. I let that sit and usually pour off the extra dye and then add the soda ash mix.
OR I'll fold the fabric, and put in a shallow container, pour the dyes on, stll pour off any extra (like the black that was at the bottom of your container) and then added the soda ash mixture.
I never let them sit for 24 hours though. In a warm room, anywhere from 45 minutes to just a couple of hours in plenty.
I also don't use synthrapol, (or however you spell that one), I use either Dharma's textile detergent or regular Dawn liquid soap, both work perfectly.
Hope that helps some.