While it can give you some insight, I'm wary of this kind of state-level analysis of migration, since the conclusions aren't necessarily the same if you look at movement on a more fine-grained scale. States are big places (well, some are). Texas is not very wealthy on average, for example, but some parts of it are much wealthier than other parts. And people are generally moving to the richer parts, not the poorer parts: the largest population increases are in counties that rank in the top-50 highest-income counties in the country (Collin County, Fort Bend County, etc.). Therefore assuming someone moving to Texas is moving to some kind of 'median Texas' is an oversimplification that might produce misleading conclusions.

It's possible people are still typically moving from wealthier to poorer areas (e.g. from Manhattan to Dallas), but we'd need more specific data than state-level flows to conclude that.