w0x0f, thanks for the reference.
So, there might be less than 3 minutes of time between when the King Air begins his roll and I land, so it makes no difference if I'm number two. The controller can waive the 3-minute rule so long as I can maintain visual separation. Since I was not stop-and-go (and therefore not an intersection departure), the controller did not necessarily need to apply the rule in 3-9-7-b3, but he did anyway.
I talked to another instructor today and he said there was a meeting about a month ago, before I started here, about the "maintain visual separation" instructions. The controllers talked about the instructions as they pertain to wake turbulence, and used the King Air as an example, since its gross weight is 12,500, so those wake turbulence rules apply to the King Air. I'm learning. Slowly.