Hmmmm. I have to wonder about the need for parentheses at all.
He made a promise to his colleague Mark that he will be there in time for the meeting.
When you use that, in this case, you do not need a comma at all.
If, however, you change your word order, the commas are then necessary:
He made a promise to Mark, his colleague, that he will be there in time for the meeting.
This second sentence is a bit more ambiguous because the subject of the dependent clause may or may not be seen as the same subject of the independent clause.
Please note we say either "on time" (meaning at the time agreed upon) or "in time for xxxxx."
Also, why are you saying "makes" here? Was the promise not already made?