If upgrading is enabled, the game checks condition for every garrison/patrol group:
100 - MaxPlayerProgress + Modifier < Priority
If this condition is TRUE, then this group starts upgrading admins, for every admin there's a chance Random(Priority) to upgrade every iteration (every time strategic AI evaluates decisions), so group with priority 100 will upgrade all admins, group with priority 50 will upgrade 50% admins every time etc. On Insane difficulty level all admins are upgraded with 100% chance.
So, if we have a group with Priority = 100, it will start upgrading immediately when Queen becomes aware of player, group with Priority = 50 will start upgrading at 50% progress.
You can modify it with UPDATE_GARRISON_ADMINS_PROGRESS_MODIFIER and UPDATE_PATROL_ADMINS_PROGRESS_MODIFIER, so with positive value groups start upgrading later, depending on their priority, with negative value groups will start upgrading earlier.