Does Mexico count immigrants who become Mexicans as immigrants (surnames, resident, European)

[SFVsocal]

I'm studying about immigration to Mexico, and I'm just wondering if back then and even today, if Mexico counts people who weren't born in Mexico, but become Mexican citizens, as foreign or immigrants still.

for example, British immigrants in Mexico.

http://i.imgur.com/3TR6p2L.png

There were nearly 100,000, then 30 years later, nearly 5,000. Did they just leave Mexico in mass numbers, or did they become Mexican citizens? (link above has picture of what I speak of)

I've seen Mexicans with English and Irish names, but obviously not a lot. I did hear that one president named Obregon had his original surname as O'Brien, but changed it.

I also read an article written by this Mexican girl who was talking about race in Mexico, and said that some European immigrants and white Mexicans with non-Spanish surnames changed it to Spanish sounding ones or Spanish ones become "Mexicanized", now how Germans did in America.

thanks..