The one and only thing that triggers migration (as it has since well before mankind walked erect) is photoperiodism - the relative amounts of daylight and darkness over time. Food availability and weather have nothing to do with when they leave north Texas. These two factors only determine the pace at which birds migrate.
Photoperiodism, usually called 'day length', also triggers leaves to grow or fall, flowers to bloom or go to seed, animals to hibernate, insects to become active, wild animals to have babies, and so on. It's been this way millions of years before Man appeared on earth.
So when your neighbor takes credit for causing flowers to bloom since he added a certain chemical to the soil, or he cautions you to take down birdfeeders for fear of "trapping" birds for the winter, remember that the earth tilting and revolving on its axis, making days shorter or longer, is the one and only cause.
An example in north Texas is the Robin. Due to Texas' slightly longer day-length and relatively mild winters, Robins (and several other birds) think of this area as "the South". So the Robins from up north migrate here for the winter. And local Robins stay right here. As a result we have more Robins in north Texas in the winter than the summer. Thanks mainly to photoperiodism.