I would hazard a guess that if you divert when at MIN RESV fuel you will often arrive with <30mins. On various diversions it has often taken 5 mins to get a clearance to start the diversion. If it's close by you then have to brief the arrival and approach at diversion quickly. If you've been in the hold at destination this should have already been done and some sort of FMC programming done for the route. You can create a 'route discontinuity' after DEST RWY and then insert the diversion route to IAF. When I did this technique to a budding 3000hr potential captain he remarked he'd never thought of that nor seen it done. (back to trained robotic SOP monkeys).
Anyway, you were not in the hold but divert almost on arrival as you are given an EAT and have little extra. It will be very easy to arrive at diversion with <30mins and then get a hold due to other diversions. In some circumstances diverting when at MIN RESV is too late, but that is a captain's decision and guidance on that is not often included in command courses. Shame.