That is one version of implication. The implication could also be that a time component isn't stated explicitly. He drove her to university. Time passes. Now

That is one version of implication. The implication could also be that a time component isn't stated explicitly. He drove her to university. Time passes. Now it's "afterwards" and Sue is done with her classes and they go back home to drink tea. For all we know Joe had a cup of coffee while she was writing an exam but because they live so far from university it made no sense to go home and come back to come pick her up as it might take an hour to drive each way and the exam was 2 hours.