I have some objections to your basic premise, and you may want to describe the alien society in a way to show reasons why my objections don't apply to the situation in your story, which thus will be highly unusual and unexpected.
I find the premise that the alien world would be more advanced than 21st century Earth for many hundreds, thousands, or millions of years, but never bother to explore or colonize their own or other star systems, and then suddenly develop interstellar travel when their home world is threatened, and seek to migrate to Earth, is deeply flawed. I always hated it when pulp-era science fiction stories used that plot, and I don't see much use for it in 2018.
If the aliens are anything like Earthlings they would gradually explore and colonize other planets in their solar system, and build space habitats, and eventually have thousands of times as many people living in space as on the home planet. So if a disaster threatens their home planet, the population of it can seek refuge elsewhere in their solar system.
And they would eventually also explore and colonize other star systems. And thus if a disaster threatens their entire home solar system, the population of the home system can seek refuge in already colonized solar systems and explored but as yet un colonized systems. And unless they have a faster-than-light drive their star ships will have to keep them alive for decades, centuries, or millennia, and they will have a proven ability to create livable environments in outer space - their star ships will be more or less artificial space habitats with interstellar drives attached. So they won't have much need to experiment with how well they can survive on Earth if the conditions on Earth are only partially in their comfort or survival zones.
So you might want to consider those reasons why your premise is so improbable and come up with reasons why my objections to it do not apply.
For example, maybe the aliens only have 21st century technology but do have psychic powers, that enable them to locate the borderline habitable planet Earth and teleport themselves to Earth with just the clothes on their backs (if they have backs) and a few tools they can carry.