What ISN'T mentioned in 'classes'...
One of the primary rules of range safety is "Keep the muzzle pointed downrange, or in a safe direction."
Great idea. For whatever reason, I just had to draw down on a malefactor posing an immediate, deadly physical threat in the main passageway in the local mall. Which direction is 'safe'? Could someone answer that for me? In about forty-five years of carrying a sidearm, the only answer I have is to point it 'up' or 'down'. North, South, East and West are all taken up with bystanders, potential victims and other bits one does not want to shoot without serious provocation. Mr. Ettin's photographic suggestion seems reasonable.
Good heavens, yes; scan the whole area to make sure the malefactor doesn't have a partner, a safety man, a getaway driver or nanny in attendance. One might also make mental notes about witnesses, if possible.
Don't point the weapon at anyone intentionally - to single out that person - unless that seems to be the 'significant other' in the malefactor's scheme. But 'turn' one must just to check the area.
Holster without looking? Great idea, again. Easier if one is carrying an open type belt holster; not so easy if carrying concealed. I commonly wear an open top holster with retention strap under a jacket. I can holster without looking, but I have to feel around a bit. Normally there are no bonus points awarded for 'speed of return to holster'. Don't get panicked about it. Just get the pistol put away when it is prudent to do so. Preferably without discharging any more rounds.
This may include moving to what in boxing is called a 'neutral corner'. Not 'gone', but away from the open and in a position to maintain an eye on the scene. One does not want the casual passerby to pick up or move evidence, like the malefactor's weapon. But as previous noted by Mr. Ettin, don't imply by action an intent to 'flee'. Obviously, this is colored by a lingering firefight or other malefactors present.
Normally, one will meet the local authorities shortly - who knows how long - after such an event. One should call for both LEOs and EMTs and give a brief regarding what happened. How many wounded, what sort of wounds (in general and to the best of one's ability; not everyone speaks anatomy or trauma care) and if hostilities have concluded or not. If hostilities continue, brief dispatch about location of villain or villains and from which direction approach is safest.
When the authorities show up, expect to be handcuffed and disarmed. Just expect it. Have your license and ID somewhere handy - like a shirt pocket - so as not to 'dig' for it in pockets. When they ask, tell them where your sidearm is located. If they are nervous, they probably don't want you getting it out for them.
Surviving a shooting is more than just shooting ability. One must not panic and the best way NOT to panic is the same method of not jerking the trigger; concentrate on what needs to be done. One needs to work this out prior to the encounter.
Frankly, I would probably need to use a restroom. I tend to overactive bladder when emotions run high.