Progressive Politics

Also

https://en.m.wikipedia.org/wiki/Operation_Wetback

However, voluntary repatriation was far more common than formal deportation and federal officials were minimally involved.[5] Some of the repatriates hoped that they could escape the economic crisis of the Great Depression.[9] The government formally deported at least 82,000 people,[10] with the vast majority occurring between 1930 and 1933.[5][11] The Mexican government also encouraged repatriation with the promise of free land.[8][12]: 185–186 

This makes it seem like many of them wanted out of the US already, and Mexico was more than willing to receive them.

Edit: The page also says that people were blaming Mexicans and making them the scapegoat for the reason why they were dealing with the great recession. It seems that many were already wanting to move to Mexico due to the recession coupled with the promise of free land. There were still a lot who were deported forcefully against their will.