The reason Americans became immigrants to former Spanish owned Tejas, and then Mexican owned Tejas, is remarkably simple. For those Americans willing to become members of the state church (RCC) they got a great price on fertile land ~ and both the Spanish and the Mexicans had a great admiration for the American ability to take raw land, live under horrible primitive conditions, withstand the worst weather on the planet, and produce crops like there was no end.
One of the things that helped Americans settle the area was also simple ~ the earlier Spanish settlers had brought in cattle, pigs, chickens, goats and other domesticated animals, and they thrived even without humans around mending fences. American settlers in Texas ate well!
Mexicans imported Germans to act as a buffer to the Apache. Then all of a sudden there were 14,000 Germans in Texas so they started paying the Apache to try to run off the Texicans.
Americans were known to use a lot of "Green-Gro" fertilizer, hence the name "Gringos".