If you want to look at why this happens in the real world, it's resource extraction. You see this in the European era of colonial (a lot), but even in modern times with powerful countries such as the United States backing regimes they don't necessarily like (such as Saudi Arabian Royal Family), against their rivals in the region because Saudi Arabia ensures them access to oil. Similar dynamics played out in Colonial India, in the "New World" with native tribes, in Africa (are playing out even today in Africa).
Why does this happen? I mean, if the Aliens are more powerful, why not just wipe out humans to get to their resources? Well the United States Armed Forces definitely have the capability to wipe out every country in the Middle East and "take the oil." There are several reasons we don't. The biggest is probably that public opinion just wouldn't support it. Nobody in an educated and open society (or at least very few people) want genocide and or national piracy openly committed in their name.
LONG SIDE NOTE: You could argue that in war time it would be accepted, or even in the wake of a 9/11 scale terrorist attack, but the world is too globalized now, too instant, too visible. What kind of support would the "moral bombings" of WWII had had if there videos in full color of charred bodies streaming live on youtube at the time. But anyway, unless humans attack your aliens, this whole side note is a mute point.
The next more cynical reason is that dead men make terrible laborers. It's just a more efficient use of resources coerce or pay people to work than kill them, and if they are trying to kill each other... well backing one side is an excellent way to get them to work for you under threat of annihilation without actually having to even threaten to annihilate anyone yourself.
The believability of this really depends on the aliens themselves. If they are James Cameron Alien type monsters or Invasion of the Body Snatchers single mind ends just means no regrets type aliens, it falls apart. However, if Alien society resembles our own with shifting political dynamics, value of individual life and limited resources: totally believable.
Becky Chamber's novel "The Long Way to a Small Angry Planet" (which I'd recommend as fun read) actually revolves around this very dynamic. A powerful Galactic inter-species Federation(? forget exact term she uses for governing body) admits a faction of a new race into the federation (which gives this faction a defensive treaty) even though they are at war with other factions of their own species to gain access to resources within this species' territory.
As far as which side the Aliens choose to back: it's either going to be which side the higher ups perceive as being in a better position to begin with (nobody wants to back a loser); which is more willing to work with the aliens, or aliens think would be more dependable to work with; which is percieved as the good side in the realm of alien public opinion... probably some combination of the three.
