If you choose your protagonist(s) to be civilians, then in their perspective, King Sombra's invasion of the United States would seem to them as if they were experiencing a full on Zombie Apocalypse. Mind-controlled Humans would be no different from a Zombie and despite being forced to fight their own kind against their will, they will be shot at because the survivors think that they're so far in their mind control that they're beyond saving not to mention they're extremely violent and aggressive.

Unlike a viral Zombie infection, the survivors and military have a single individual to put the blame on and curse at with their dying breaths, King Sombra himself. The "Son of a Bitch" who took away their loved ones and ruined their lives.

Their story would start off at the moment Sombra launches his attack on the three cities of the Northeastern megalopolis, Washington DC, Baltimore or Philadelphia. like this:

If it's someone in law enforcement, it starts off like this:

I didn't mention Boston and New York because New York in my scenario is the turning point where Sombra's advances would be successfully halted and pushed back.

There are two options on what aspect of Sombra is controlling the Human mind-slaves:

Mind Control:

Unlike the mind controlled ponies, mind controlled humans are extremely feral and rabid beasts. Thrashing about uncontrollably and screeching in an inhuman and animalistic manner They are the vanguard of Sombra's army of mind-slaves and charge in first to sow chaos and spread Sombra's dark influence like a virus before the mind slaved ponies march in after them and sweeps away anything left. This would be similar to a "Fast" Zombie apocalypse similar to the quick nature of the spread of the Solanum Virus from World War Z.

Sometimes there would be so many attacking that these horrifying scenarios occur where under Sombra's control, they overcome defensive structures by continuously Zerg rushing them until they start piling up on themselves and then flowing in and overrunning the breach like a massive torrent of water:

The main difference between the Mind controlled Humans and Mind controlled ponies is that the humans possess no helmets are and directly controlled by Sombra himself, meaning the only way to break them free is to kill the King of Darkness. However, as there is no way to reach him or even harm him, Humanity is left with no other option but to kill their own friends and family who have fallen under Sombra's dark will. By the time they do figure out what was really happening to those Humans in Sombra's army, Millions of those poor souls would have been slaughtered by the time Sombra is defeated. The ultimate "Stop Hitting Yourself" move.

The thing about him controlling an army without helmets was shown in the start of season 9:

Possessed by Umbrum:

Alternatively, the Humans pressed into his Army could also be possessed by the Umbrum from the IDW comics canon. An ancient race of horrifying wraith-like monsters of which King Sombra is a member of this race.

Like Sombra, they would also be invulnerable to physical attacks on account of them being evil spirits.

This would better explain why they have such a feral and rabid behavior but would also make them similar to deadites from evil dead. i mean imagine these:

Possessing a Human and turning them into:

This video would illustrate the process of how the Umbrum would possess and take over their victim's body would look like.

Their unfamiliarity to the Human form causing their hosts to contort in unnatural movements until they are fully possessed.

The protagonist(s) would have to spend two months in hell trying to survive in conquered territory before the US Military gathers enough of it's forces to push back and retake the northeastern seaboard.

like imagine this band of survivors wandering through the husks of what were once Washington DC, Baltimore and Philadelphia. All have that familliar tell-tale sign of Sombra's presence and influence over his domain. Dark Crystalline growths erupting from almost everywhere

This thing actually does happen in the show, Sombra's presence on an area being marked by dark crystal shards erupting from the ground/floor.