That scene does seem odd. During the rest of the movie, it seems as though when Phil falls asleep, the day resets. I would think the same thing would happen when he dies.
It could be that the day resets at a particular time, like 4 in the morning the next day. We never see Phil awake at 4:00 AM. (It doesn't reset at midnight; Rita and Phil are together one midnight, and time just keeps rolling forward.)
Most likely, the director wanted the audience to think that the day resets in a magical way, at the "appropriate" time.
From a film business perspective, it's possible that the scene of Rita and Larry in the morgue was added on after principle shooting. That is, some studio heads or test audiences watched the movie without that scene, and their main question was, "So does Phil really die when he drives the car off the cliff with the groundhog?" That scene could have been added to clear up that yes, he actually does die. However, I couldn't find anything about that online.