Grout Colorant is applied by painting over your existing grout. This can be a very tedious process; not forgetting back breaking.
If it is for your floor tiles where there are lots of traffic, it may not that durable.
Alternatively, you could get your contractor to remove the existing grout. White cement can be easily remove as compared to the grey cement. Then re-grout with your preferred colour grout. This will be longer lasting.

From what my reno contractor told me previously, it should not cost an arm & leg. 
He did that for one of his client when he was renovating his house. Since he was carrying out the other renovation work at the same time .... That was replacing the existing floor tile grout by the developer.
Anyway, it will also depends on the area affected and the man-days required.