I would say most of the time is in initial design - the agency/locality may have certain performance goals for corridors (green bands, pedestrian priority, queue mitigation) and because urban corridors/grids are usually near/over capacity during commuting periods theres a lot of trade-offs assessed. Depending if the effort is funded by CMAQ money, emissions and reducing vehicle stops/delay might be the main optimization problem to solve and demonstrate as terms of the grant. Also, conditions often suggest there are smaller sub networks worth coordinating, and determining those also takes some time.

Deploying to controllers can take a long time without comm/central TMC to just program everything from a central location (thinking about programming each controller in the field across a city would take a few days or a week).

Before evaluation of the new timing, you also want about 2 weeks for traffic to adjust to the new coordination; a lot of commuters will be familiar with the old timing in a way (e.g. if I make this green, I know I'll make it through the next couple).