The first, and most difficult part, is that you are going to come to a halt, and then, seemingly, enter a time warp. You (passengers) have nothing to do (other than panic), but we need you to stay seated initially. Up the front, we'll park the brakes, tell ATC something (but probably not evacuating yet), and a PA will be given "Attention, all passengers remain seated and await further instructions". That tells you to stay put, but it also tells the cabin crew to stand up, look out the windows, and otherwise mentally prepare to evacuate.
In the coughpit, we'll carry out the actions (at least the initial ones) for whatever caused the abort. If it needs to jump to an evacuation, then we go to a paper checklist (which the FOs keep by their side). It basically has us park brakes, tell ATC, shutdown all engines and APU, push ALL of the engine (and APU) fire switches, and to fire the extinguishers as required. Then we can evacuate.
If you go too soon, well, firstly it might have been unnecessary, but secondly the other engines are still running, and they are dangerous, whether you're in front or behind.