The preposition ‘with’ relates ‘your colors’ to ‘precise’ ; English is often quite flexible in the use of these words, and ‘in’ or ‘about’ could also be used : ‘ If you need to be precise in your colors . . ‘ ‘ If you need to be precise about your colors . . ‘

A little more context is needed. 'with' is the best preposition in the sentence you have. However, likely better would be something such as If you need precise color ... If you need your colors to be precise ... For precision color ...

With means with as it always does and it doesn't really change according to context. with (preposition) - In the company of; accompanying. - Next to; alongside of. - Having as a possession, attribute, or characteristic. Could you please bring that sentence in a context so we can understand better what you mean?