My understanding of malaria and its spread is essentially the winters are cold in the states and kill off all mosquitos in the winter. The larva (or whatever the correct term is) don’t carry malaria, so the mosquitos must grab it from an infected animal.
So the warmer the states get, the warmer the land south of the states get. More and more mosquitos survive winters closer to the states, and so smaller travel distance.
But based on what you just said it seems that understanding is not actually how it works?
I didn't do the research and am not the expert, but essentially:
Temperature impacts mosquitos in several ways that change their effectiveness as a vector for disease.
The temperature during egg/pupa/larva stages impacts adult body size and fitness of the mosquito. That in turn tends to impact total lifespan.
A change as small as 2 to 4 degrees C can add or remove more than a week of lifespan for a mosquito (huge change, the average lifespan is 10-14 days), and the longer a mosquito is alive, the more likely it is to become a vector for malaria (and other diseases). For malaria in particular - the life cycle of the disease means the mosquito usually needs to make it at least 10 days to become a vector.
Throw on top that changes in temperature can change the feeding habits (shift them in time to make mosquitos more likely to feed when humans are out) and that parts of the southern US are now considered viable habitat for these subspecies and you get Malaria.
They do still need to interact with an animal/person carrying malaria during their adult stages - and the general strategy in the US is still to contain and treat those carriers.
We just expect it to get much more expensive as these mosquitos become more fit for our region.
So the warmer the states get, the warmer the land south of the states get. More and more mosquitos survive winters closer to the states, and so smaller travel distance.
But based on what you just said it seems that understanding is not actually how it works?