Just noticed this with any pistol's quick draw holster where the animation is much faster, but the time it takes until you're allowed to fire is the same as without the holster.
Easy way to reproduce this is to hold whatever your fire button is while the character is switching through weapons, the weapon will fire as soon as its allowed. For guns with holsters you'll notice there's a delay between when the animation ends and when the shot is fired. This delay does not exist for pistols without quick draw holsters.
I only thoroughly tested this with Security pistols, but I believe it exists for insurgents as well.