Let's start by putting this question on a better footing. There is no evidence of "haste," the migration was not "instant," nor is the original question "purely mathematical." ("What do these p-values mean individually about those parameters?" asks for a statistical interpretation, not about the mathematics of regression.)
Timeliness in migration is a good thing. It can be confusing when a question accumulates comments and answers on one site and then is moved to another. That the regression question was identified and migrated within an hour of its posting testifies to the watchfulness and care of the math site's moderators. Let's not attribute their dedication and professionalism to "haste": that's an unfair, unwarranted characterization.
A sounder, politer way to raise the concern expressed in this thread might be, "help us understand how the math and stats communities make decisions to migrate questions between them."
This is something that high-rep members and moderators in both communities have to consider routinely. Ultimately each decision comes down to determining which site will serve the question better. The math site excels in obtaining rigorous, carefully qualified, purely mathematical answers to precise, well-framed questions. The stats site does well at explaining applications, interpreting results, and helping the OP find a way to ask the question they really meant to ask, but didn't know how.
Some questions sit on the boundary. This is natural, given the mathematical theory that imbues all of statistics and the existence of mathematical statistics as a branch of pure mathematics. In those situations, either site would be a good home. Thus it's not a problem if some of these boundary questions get moved to the other site. As a moderator of the stats site, when I encounter such questions I may make a quick search of both sites to see where similar ones have been asked, how many people have been interested in them, and to gauge the qualities of answers they may have gotten. I want the question to go where it will get a great answer, quickly, not just a "good" or adequate one.
Two aspects of a thread that would seem to be part of migration decisions are actually of little import. The presence of answers in itself means little. However, if either (a) a question has been around for a few days and has accumulated no answers or (b) a question is collecting answers that are clearly off the mark or less than helpful, then that suggests a need for migration. Popularity (measured in votes, views, or favorites) is irrelevant. A question can be clearly off topic on one site and still be popular there. Off topic questions ought to be migrated, closed, or modified to be appropriate for the site they're on. This of course is an ideal and in practice we don't always get it right, but we come close.
Incidentally, the migration process automatically moves all comments and answers along with the question. It has to: where else would this ancillary material go?