I made varigated yarn with KoolAid, and didn't have a problem with the colors running into each other. I laid the yarn out on plastic wrap, squirted the dye on it, then folded the plastic wrap over. Then, it went into a glass rectangular casserole dish and into the microwave. I didn't cook it on the stovetop, so I don't know what would happen with the colors if you did that.
Good luck with your dying! It's a lot of fun, and so easy!