First, while I've had access to these for ten years, one was personal and one belonged to my previous company. Neither was used with umbrellas in "reflective" mode, where the light travels over the flash unit, before. I just received the second unit (no longer needed by the company) and started experimenting with umbrellas in reflective mode this weekend.
I've thought of a quick way to test this out: I'll use flash at the angle that gives the yellow blob with an umbrella in reflective mode, then take a second shot with the flash at exactly the same angle but shooting through the umbrella (so the light doesn't go over the flash unit body).
OK, I took the shots, using two different umbrellas in reflective mode (one Wescott, just bought yesterday, and one unknown brand at least 5 years old), and the Wescott in shoot-through mode. Here are the shots:
Wescott, reflective

Old umbrella, reflective

Wescott, shoot-through

So, there is a clear yellow pattern in the two reflective shots, which differs between the two umbrellas. And suprisingly, there is a slight, yellow, blob in shoot-through mode. Note that the room is fairly small, so there's a lot of bounce from using the flash in shoot-through mode (due to some reflection and spill), which could be lighting up the flash unit enough to create the lighter yellow blob.
Any other ideas?