Based on what I could find, it seems that a lot of Vietnamese people went wherever there was better sponsorships since a bunch of people were fleeing the Vietnam War. California and Texas happened to have better conditions such as existing Vietnamese communities, better safety nets, etc.
New York's Vietnamese immigrants in my experience were largely ethnically Chinese and likely don't identify as Vietnamese. Growing up, I knew several families like this. The only real distinguishing factor was that their Chinese surnames were spelled according to the Vietnamese way (Tran for Chen/Chan, Luu for Liu, Phung for Fung/Feng, Ly for Li/Lee). Otherwise they considered themselves part of the Chinese population.
Assuming this quiz is about ethnicity, and not nationality, it seems like it would be correct not to consider them Vietnamese. There are Mandarin-speaking, ethnically Han Chinese communities in Vietnam, and because of ethnolinguistic background, they tend to consider themselves Chinese, even if they are Vietnamese nationals born outside of China. The quiz probably should clarify what metric is used to categorize what makes a person "Vietnamese".
It's census data, so self-reported. People are identifying themselves and that doesn't necessarily have anything to do with birth country as people have pointed out. The source has methodology with all that info.