Brief look at this is that they have supposedly been races kicking around our planets history for a very long time, as people have been seeing in historical reports.
So lets just pick one race with no Human concepts of motivation (as in money politics, I know it's hard to do.) and they have had some disaster on there home world/Dimension.
If they are smart enough to design these craft to travel over distance or time (or both) and can genetically engineer life forms.
Why have they not just built massive for a better word Ark ships?
Or travelled back in time to fix their planets problems?
Tripped back in time on the planet Earth pre humans and just removed us and altered the planets eco system to suit them?
If they are being victimised by another race and using our planet as a place to hide, again use the time travel card and go back or forward and fixed it so this race never existed etc?
Or eco-formed another ball of rock, because they have had the time, or used time travel as well, both ways you could seed multiple worlds at the same time and see which evolves correctly and then move your population on too it.
If there are as many dimensions out there as they say, think of the space contained in each one (now your headaches) they should find a place to call home.
If the worst came to them they could DNA engineer their race to adapt to the new conditions?
Again if all possibilities are out there and they could travel each route but not travel back in their own time line to fix and event find the closest before the problem and shift your race back one (Over crowding and duplication of the same population on the planet will be a problem to discuss). But if it was a race or disaster coming to that part of space you could still move them back to an alternative where it didn't happen.
Say for example it was like the old trading ship days when different cultures sailed with the popular one around the globe because of knowing that they major culture was well received in those countries and you would be able to trade without to much difficulty and they also had better protection. A few used to get shipwrecked on countries that were not their own and they ended up living with the local population, whether due to storms or ship problems that could not be repaired.
So maybe these craft/aliens could be in the same situation, missing from the major part of a fleet not of the entire same race etc so just stranded trying to find a way to stay alive.
Even wilder theory that the craft they are in are automated craft not designed by them and they have been separated from the main fleet and end up with races that can't fly them.
Then you could launch into even odder theories of time storms, quantum fluxes affecting these craft.
The list goes on and on, so I feel if they were manipulating the atmosphere for their benefit, they have chosen the long way around.
Last thought it could always be The Emperor Ming (
Flash Gordon (1980) - IMDb) playing