Nice table from Miller, Foreign Born in the United States Army During World War II, With Special Reference to the Alien, INS Monthly Review, October 1948.
During World War II, the United States was very permissive in allowing non-citizens to join the military and was then permissive in allowing citizenship for those who served. This table says that during the war, 109,382 members of the armed services were naturalized. Of those, 9,741 were from Mexico.
The way I understand it, our uncles were born in the US. They returned to the states to sign up before they were drafted.