If you are not in engineering, it is difficult to transfer into an engineering major. There are high requirements, you only have access to general courses that may/may not count for each respective engineering discipline. Furthermore, the required math classes he will take for Mays will not count towards engineering. So he is looking at taking business calculus and if he wants to switch into engineering, he will have to go and take engineering calculus.
I love A&M, but if your son wants to be an engineer, he should go to UT if they accepted him and A&M did not. He probably would have an easier time transferring from UT engineering into A&M engineering than he would from Mays into engineering if he decides he wants to be at A&M. Best of Luck!