Flinching is always before the shot goes off though, bullets go so fast bumping the barrel of something like an AR-10 after primer ignition won't do anything at that distance.
i mean, he's saying ".380" which is usually shorthand for 9x17mm / .380 ACP / 9mm Short. anticipating recoil will usually dip the muzzle low at the shot because the wrist is breaking immediately prior to the trigger squeeze in order to "absorb recoil" and i've seen this pretty commonly with smaller, snappy pistols and pistols that have a sharper recoil impulse than typical combined with a lighter than typical profile: PPK/s, PM, Glock 33, et c.
you can also get lower then expected on a target if you're trying to "push" the gun forward with the strong hand's web during a presentation especially from holstered as there's a reflex there when grasping an object to hold it tighter when it's further away from the body when you aren't consciously trying to let it go.
a flinch doesn't always happen prior to a shot, but alongside it. in the first form i've observed it result in "wiggling" the front or rear sight, causing a loss of focus on the target and an over emphasis on the trigger break, resulting in scattering the shot. another form is with attempting to under or overcorrect trigger engagement and this tends to pull shots left or right. the last one is changes in grip pressure where the whole hand is involved in the trigger squeeze and this can lead to stringing vertically, which is close to what's being described.
between recoil anticipation and "whole hand" trigger squeezing (which can apply a pressure differential to different parts of the grip and subtly change the point of aim as the trigger is pulled), for smaller firearms it tends to be recoil anticipation as the snappier recoil in experienced shooters can lead to trying to reduce the impact to the web of the hand. this develops over time as a new shooter develops bad habits, while the latter is an experienced shooter trying to control the firearm in a way that doesn't work for smaller guns.
at least that's my theory on it. without seeing video or targets it's tough to say one way or the other. one good thing to try (and everyone likes to shoot more) is to swap to a very similar gun in an alternate caliber, or the same caliber in a differently shaped frame. like if you're shooting a single stack .380, try a single stack 9mm. see if the problem persists. it might boil down to a combination of how the frame interacts and supports/resists the palm while firing, to the caliber being a little too snappy in the particular frame that it's in.
i doubt the other two common causes apply: horribly aligned sights (this would be really obvious and relatively consistent), or something specific to the ammunition (inconsistent loading).
if he was talking about a rifle, then yeah i missed that and it wouldn't be anticipation.