Color hair is heavily chemically processed that causes the hair to shed and tangle really quick. It's very important to condition your hair at the first sign of tangling, 2-3 times a week is recommended. Serum is also good to use on color hair.
Color hair cost more but the quality is usually not worth the extra cost.
The care for color hair is hard to outline.
The best answer is to condition your hair at the first sign of tangling.