Actually birth rates are way down in Mexico and the rest of Latin America. Not as much as here, but not what they used to be. When people have the option of birth control many will use it. Here’s a site where you can graph the birth rates of countries around the world. These are just from 2000 but the longer term trend is the same.
https://www.indexmundi.com/g/g.aspx?c=mx&v=25
Guatemala--2.77
Honduras--2.67
El Salvador--1.87
Canada--1.60
US--1.87