Well, note that that map is where people tend to move some number of years after graduation, not 'where do all college-educated people move'; the latter would show more migration towards the Sun Belt.
This map is from 2016, and the Axios map I posted above is from after COVID (2022), but there indeed might be a difference as to where people move mid-career as opposed to where they go to start it; it seems like there's a preference over time for moving to warmer areas. I think this map is already out-of-date, and the changes to it make it resemble the Axios map more; the Axios map is also probably a preview of what I think trends will look like in the future, rather than what trends are now. (Also, it would take a lot to make TN vote Democratic! Also, TN is still net losing college graduates on that map! Also, I don't really think a division based on education levels is very long-run sustainable!)
But, yes, if something like current patterns continues for another decade or so TX will probably flip blue. (But it also starts to make the sustainability of Democratic trends in places like AZ/VA look questionable).
Note that, because this codes people's state of origin as "where they went to college", states that attract lots of out-of-state college students (particularly VT/NH come to mind here, but perhaps also VA?) are disadvantaged by the metric; I think VA would look much better if you coded state of origin as "where a student went to high school". OTOH lots of out-of-state students go to college in CO, so CO appearing here as...the single strongest state in the dataset, after DC, is totally bonkers. (DC's own performance is also bonkers, since many people travel there to get educated). It must be the case that CO is continuing to very rapidly become much more educated; this makes the 2020 trend much less surprising. No other state puts in a performance remotely like CO's, and only NY and WA are really even comparable. (And CO also puts in the strongest performance of any state on the older NYT map about the migration patterns of older college graduates! Amazing stuff.)
It's also interesting to note that these states don't really line up with which ones are growing overall. CA, NY, and IL are all likely to lose House seats at the next reapportionment, but they're all gaining college graduates looking to start their careers. FL has insane growth (and actually if you look through the data FL is very good at keeping college graduates who graduate there -- in fact it's third nationally for doing this -- but it's stunningly bad at attracting out-of-state college graduates to start their careers there. This fails to square pretty hard with my own experience -- I know multiple recent college graduates who have moved to FL -- but then my circles are consistently weirdly Ameriright in ways that don't really extrapolate to the whole country. But I'd take this whole dataset with a grain of salt).
First off, looking through the paper your previous chart is taken from, I notice that the data are aggregated at the CBSA level, so I'm not sure how they were separated out to create the state-level map. The appendices describing the methodology don't say. This is significant because it's unclear if someone who lives and works in Jersey City whose LinkedIn page lists them as "New York City Area" would be properly classified under New Jersey, or even whether this would be able to accurately account for commutes that cross state lines. (Presumably most people list where they work on LinkedIn, not where they live.)
In part for this reason, I'm not inclined to draw any conclusions from what the chart says about Virginia. Like all the states to its north, Virginia experiences a fair amount of attrition to New York, but, in addition to that, Virginia's largest metropolitan area is not centered within the state. Plenty of graduates from Virginia colleges work in the District of Columbia or in that broader metropolitan area; this does not mean that Virginia has lost these graduates, especially if they continue to live or work in the state. (If my hypothesis is right and this study treats anyone whose LinkedIn profile says "Washington, D.C. Area" as being in DC, then that would also explain the otherwise remarkable DC figure: there are a lot more people who work in the region then there are people who graduated from colleges in the District.)
As regards Florida, I am always taken aback at the South Florida metro area having more people than the Atlanta metro area, because I don't really know anyone who lives there. (When I spent a night there on a layover late last year, I had to get a hotel, whereas in almost any other city I might stop over in I'd have a friend to offer me a couch to sleep on.) I do know three people who moved to Florida relatively soon after graduation, but all three were in fields with an unusually small number of job openings (baseball, print journalism, medical physics) and none stayed more than a few years before moving elsewhere. None of them came to Florida already having friends there, which is key to understanding the data.
The reason that Tennessee loses graduates on aggregate is because quite a few Tennessee graduates move to Atlanta. The reason that Indiana loses an enormous number of graduates is because of the annual flood of Indiana graduates to Chicago. By contrast, there are no large colleges outside of Florida that are anywhere near a major Florida city. Most people moving to Florida after graduation will have to do it alone, without the benefit of a large number of friends from college making the move with them and forming a ready-made community in the new city. The result is that Florida graduates stay but other graduates don't come in large numbers. The same factors hold for California, but California has so many job opportunities for educated workers that my guess is that this effect is washed out. In the case of Colorado, the state is so irresistible to 23-year-olds that this effect is certainly washed out.
