Premeditation can happen in an instance. It just means it was intentional. It doesn't have to be planned weeks in advance. If he stopped the car, got out, chased her down, attacked her, and killed her, he's doing intentional actions that result in her murder. At any point he could have stopped - not stopped the car, not got out of the car, not chased her down, not attacked her, not murdered her.
Also these are just the preliminary charges. The prosecution can add additional charges during their investigation, or instruct the jury at trial to consider lesser included charges. We will see what the evidence says.