Shouldn't the down-shifting follow the braking?
I was taught to smoothly apply both breaks while firmly gripping the bike. Once at a complete stop, check behind you while simultaneously "stomping down" the gears to first.
problem is if you're already stopped it's hard to downshift to 1st, esp if you're in a higher gear like 5th or 6th. we were taught to be tapping the gear shifter constantly until stopped while braking (even if you think you're already in first) and that way you know you're in 1st ready to go if someone behind you isn't stopping.