The rescue is the most technical event, it's easy to get bogged down in details and time out.
Break it down into stages and give yourself a time limit for each part.
Say it's a 6 minute time limit:
1 minute for assessing the situation, making a plan, and inspecting the tree/access line
2 minutes to set your climbing system and ascend
1 minute to set your redirect and move across to the casualty
1 minute for casualty care and attaching to your system
1 minute for descent and handover
Get the timekeeper to give you calls at 1 minute intervals.
The timings will obviously vary with the scenario. Watch how other people do it, but keep your plan as simple as possible, think it through from start to finish to make sure it will work, don't try anything new or unfamiliar to you, and stick to the plan, don't try to adjust it on the fly or the likelihood of a cock up increases rapidly.