This is one issue my current replacement suffers from, you explained it in fewer words. And yes, it is important. If the seal is tight enough to the jamb, it might not leak either way, but the lip should end up somewhat vertical when the door is closed. The creates a primary seal for the main bulb and also creates a channel to guide water away from the opening. Crude section sketch follows.
View attachment 606434
This section shows what a proper seal should look like across the top of the door with the door closed. Gray is hardtop or door surround, red is top of door, black is the seal. If the lip folds down and follows the bulb, it will tend to channel water into the joint (this is precisely what mine does).
Edit: I should add that, on my current seal, I also believe that this "lip" feature is smaller/shorter than on the factory original.
Yep, that is it. My factory one is like your drawing. But, my replacement points down.
