The Usurpations are an odd faction, mainly due to the fact that they make use of more weapons from other factions than weapons from their own own. Although it has been stated that the reason for the Usurps using human weapons is because Eric Gurt simply didn't feel like making a ton of alien weapons, I'm going to try to provide an in-universe explanation for this.
At the start of the Usurpation War, the Usurps were still unsure of humanity's capabilities and the nature of the world they were about to invade. Weapon systems and technology that worked on another planet could go completely kaput on Earth. Therefore, the Usurpations sent their first invasion forces armed with very basic weapons, such as the Alien Rifle, Alien Sniper, and Alien Pistol. At the start of the invasion, the humans actually had technological superiority over Usurpation infantry.
The first Usurpation soldiers were more similar to human soldiers during the early 20th century up to the end of WW2, when the bolt action rifle was still the standard service weapon for the infantry, and accuracy was favored above volume of fire. They had the more accurate long range weapons, while the humans possessed faster firing guns better suited to suppression. As such, numerically superior Usurpation forces with their slower firing rifles would find themselves unable to muster enough firepower and become fixated and outmaneuvered by the human tactics of fire and maneuver. The lack of reliable heavy weapons also proved to be problematic when encountering fortified positions or armored support. In close quarters combat, it was no contest. In the years leading up to the Usurpation invasion, human militaries were still engaging in counter terrorism operations. As such, they had fine tuned tactics and equipment for CQB.
The Usurpations wasted no time in adapting to human technology and tactics. They had annexed a diverse array of worlds prior to setting their sights on Earth, each one possessing environments and characteristics different from the rest. Ironically, all the changes and new challenges presented by Earth ensured that it was no different than the other planets the Usurps invaded. The alien forces were able to establish a foothold on the planet through sheer strength in numbers despite lacking optimal equipment. Now that contact had been made and territory had been gained, they could get to work plundering the caches of weapons and machinery they had inherited from the humans and analyzing combat reports to comprehend human military doctrine and strategy.
The result was a drastic change in the armament and tactics of the Usurpation military on Earth. Within months, stolen human equipment was reverse engineered, mass produced, and distributed among the ranks for use. Battle tanks and APCs were developed to mimic the vehicles used by human armies. New weapons, such as the plasma pistol and alien shotgun, were developed to counter their human counterparts and improve the performance of Usurpation forces at closer ranges. Instead of attempting to outshoot the enemy at long range with superior marksmanship, the aliens now made use of their superior numbers to outmaneuver their opponents and learned to lay down a base of fire to fixate the enemy. The alien laser rifle became a sort of squad automatic weapon for Usurpation squads. Human forces no longer enjoyed the advantage of fire superiority as often as they did at the start of the war. Instead, they now found themselves bogged down by larger Usurpation forces and outflanked, as well as needing to worry about heavy weapons and armored units. The Usurpations were no longer a ragtag group of confused, ill-equipped, and unprepared conscripts whose only saving grace was their endless supply of cannon fodder. They had become a competent, well-equipped, and capable fighting force.
There were still shortcomings of course. The Usurps still used the slow firing alien rifles as their standard issue weapon. Their infantry doctrine still involved accuracy and marksmanship despite the adaptation of the concepts of suppression and maneuvering. The average alien soldier lacked the motivation of the average human soldier fighting to defend their home planet. They could not hope to have the home turf advantage, and had to contend with the logistical challenges of transporting reinforcements from off-planet. But they had achieved a foothold, several footholds in fact, on planet Earth. Their supply of military forces seemed bottomless. By learning from their mistakes early in the invasion, the Usurpations had become a force to be reckoned with, using the humans' own tactics and technology against them.
Thanks for reading if you made it all the way to the bottom. Feel free to share your own thoughts regarding the evolution of the Usurpation military throughout the war.