When you change a dimensions to a different layer that has a different color and the dimension does not change colors, there would be a few reasons for this behavior.
1) The Dimension Style is hard coding the color. Modify your dimension style and see if the color settings on the Lines and Text tabs are set to By Layer or a particular color.
2) Sometimes you have dimensions inside of a block or external reference, these may not change by changing it on this drawing without modifying the original block or drawing.
3) Another reason is the objects are set to a particular color instead of By Layer when you inserted it. Enter COLOR at the command line, if it shows a color or number in the white box then you are inserting objects and hard coding them to that color. Select "By Layer" and click Ok, then insert a new one. Any new objects will be "By Layer". See IMAGINiT solution 00011898 to quickly change all objects to be "By Layer".