I'm no help, but it was hard to get my old bike to downshift immediately after a hard brake. I would push down, but find nothing for a few seconds. Don't know if it is a flow issue, something else or nothing at all.
Btw, nothing wrong with your rear leaving the ground on a hard brake. This is actually taught on the sport bike class given by the MSF.
Hey man, can I ask you a question? What color bike and gear do you rock? Your "emergency" problem might have something to do with cagers not noticing you coming down the road.

 

Black & white jacket, blue helmet & blue 06 f4i

I tell people they're wrong when they say assume the cage is trying to kill you. Here, they don't give a **** about anyone but themselves.

 

Contrasting colors, so it is not on you. Kills me, man. I've only been riding for a year and I have been cut off countless times. Lots of people don't give a damn, but I think the vast majority of them are just idiots. Unfortunately.
Good luck, yo.

 

Back to the question :

shifting and braking work hand in hand and compliment each other especially
in emergencies ...... so way i see it ..... potentially you were just braking while
leaving the clutch engaged .....can happen..... in practice go the dual shifting
braking scenario...... works best ,takes practice and coordination thereof.

My 2 cents Kuro ...... hope it helps