TL;DR: with the best will in the world and a totally willing populace, its probably gonna take you decades to move everyone from earth. You can't just build new sustainable environments on barren lifeless radiation swept balls of rock for 8 billion people overnight, and you won't be picking all those people up and moving them to their new homes at once.
Even assuming the feasibility of sublight spacetravel and wars of conquest, your aliens are going to have to be happy building infrastructure for angry apes for years, and years, and years.
Honestly, I expect they'll get sick of the whole thing and just kill everyone.
Would Humans be gathered in open spaces beside large population areas and shuttled off-world in massive haulers? Would space-elevators and a staggered removal over a year or two be more effective?
The principle problems are ones of scale. Even if everyone on earth were super enthusiastic about leaving, the logistics of the whole enterprise will be unbelievably difficult.
Lets say that there are 8 billion people on the planet. If you could evacuate ~22 million people per day, it would still take a year to get rid of them all, and that doesn't even take into account population growth. Probably the most efficient way to get people into space is via space elevator. If you build 20 of them, and you shifted 1.1 million people per day per elevator, you'd need to be throwing 12-13 people per second up the cable and in to space.
A million people a day is the size of the commuter traffic of a pretty sizeable city, so it is achievable with modern technology... oh, but city commuters generally come from satellite towns and suburbs, but the catchment area for each space elevator has commutes of thousands of kilometres. You're going to need to build mass transit systems to funnel people in from all over the place to your departure points.
At the top of each elevator, you'll need a way station that is capable of supporting a throughput of over a million people per day. Each of those people will need feeding, and housing. They'll need to be entertained. They'll need healthcare, and all the usual paraphernalia of civilisation... don't forget police, and jails, and criminal justice. Babies will be born at the waystations, every day, and people will die up there, every day.
Next, for each of those waystations, you need to load those million people into spacecraft and launch them to their destinations. Atlanta international airport had 107394029 people moved through it in 2018, with over a thousand flights a day. Your spaceports will be more than 3 times busier, and you'll have 20 of them. ATL has 63000 people working in it by the way, and it has ready access to the rest of the civil infrastructure of Georgia.
When you've staffed these waystations, and solved the logistic issues of the continuous movement of people through them, congratulations! You now need infrastructure that is equally as capable at the receiving end. But what about all that space in between? You've just thrown 22 million people out into the big black. Even with super ultra futuristic handwavium alien space rockets, they're going to be spending a few days out there. You'll need to house, feed, entertain and protect them during their flights. Your ships will need fuelling and servicing. Did the aliens bring enough capacity for 22 million humans a day? You'll need a shipbuilding industry.
You might not need actual space elevators (though they would be vastly easier to build anywhere in the solar system other than venus and earth) but you can't just throw a million people down in an aerobraking lander every day, unless those landers are in fact completely self-contained and ready-to-go towns for their occupants.
So now you've made a bunch of new towns, all over the solar system, every day. Great! What are those people going to eat? What are they going to drink? What are they going to do? How are they going to get power for all of the above? Hell, what are they going to breathe? Think quick, there's another few million people on the way!
So, seems crazy trying to do it in a year, doesn't it? Well, you say, maybe you could do it in ten. Only 800 million people per year! What's that, the whole of the conteinental US in about 5 months? Seems pretty easy by comparison. Now you only have to deal with a couple of million people a day. Surely that's straightfoward, just creating a brand new empty city and populating it every 24 hours. Hardly anyone need die on the mass transit systems which I'm sure will be super reliable alien technology.
They will be super reliable alien technology right?
Wait, have these people travelled using sublight spacecraft, for years, to defeat us in combat, just to spend a decade or two building trains and space elevators all over the planet they've just spent all this mindboggling amount of effort to acquire?
One wonder what on earth they're getting out of all this.