RIT dye is a "union" dye. It works well for all fibers, but requires 2 or 3 dips to get an even color.
Your socks are acrylic, so they will not shrink on you. As long as the dye was heat set, which sounds like it was, then you just need to rinse until no further color comes out of the fabric and you'll be fine. It won't come off on your legs. Any application of heat is fine: steam, microwave, oven, dryer...just be mindful of matching heat temperature to fiber tolerance.

To dye wool, soak the wool in a water/vinegar mix (acidic) to open the protein fibers to accept dye.
To dye cotton, soak in water/washing soda mix (alkali) for opening bast fibers before dying.

Creative dyers have posted that they mix prepared dye with gelatin to thicken it so that they can paint it on in specific areas, then heat set, and wash out the gelatin. Just more ideas;-)