Hi Ryan,
I'll see your dumb query, and raise you a silly answer.
My educated guess is that because that first Task has no predecessors, there is no event where the Handoff Date gets filled in, which is effectively what triggers the alert you're looking for.
So! To get what you want, I suggest you consider adding a predecessor task ahead of the existing (assigned) Task 1 called "Kick Off Project" (or something aesthetically similar) and make your automated request conversion just a teensy bit smarter: upon converting the request to a project, have it also mark that Kick Off Project task as complete, thereby filling in that next "real" Task's Handoff Date, and in turn, sending the alert to the Owner of Task 1.
Regards,
Doug