As I said before, pre 1964 there were NO quotas for the Western Hemisphere. What caused the flood is that Mexico began to develop economically, giving more Mexicans the capacity for mobility, and as Hispanic communities developed away from the border, support mechanisms were in place for friends and neighbors from the home country to join their friends and relatives.
Due to the slowing population growth rate in Mexico, and the Western Hemisphere in general, and the future growth in Mexican per capita income levels (due to development, a more middle class culture, and lower population growth), the rate of immigration from that part of the world will substantially fall off in the next 10 years.