The controller in the tower does not usually have discretion as to when to call the TMU for release. That procedure is spelled out by the center in question.
For example, ZJX requests estimated wheels up times from aircraft 30 minutes prior to departure. So, when coming out of MCO or PNS to ATL, you can call ground or clearance, and give them an ETD.
Mobile, which is located in ZHU, obviously has a different procedure dictated by Houston Center, and does not want you calling for release until beginning taxi.
So you are saying the decision on when or how to get a time is up to the Center controlling that area and not the tower? The tower just works based on what the Center is telling them?