First of all, education is very important to Chinese people. Education had played a very important role in Chinese culture and tradition. Educated people (literatus) are highly respected, admired and even romanticized. (Think about how medieval European people romanticize knights and their adventure, Chinese romanticize poor boy became successful government official and marry a princess through learning and passing exams). Study well and pass Keju (科举) exam was the only way a commoner could become government official and made something with his life. As a result, the importance of education is deeply rooted in Chinese psyche. Those who are not educated themselves want their children to be educated and get better life; those who are educated believe it's only natural that their children should do the same.
Generally speaking there're two types of Chinese immigrants: poorer people who came in either illegally or through relatives; highly educated students came in with F1 visa. Both type would play well into the mentality that their children should do well in school, should go to an ivy league university, should get into one of the "major 3" reputable careers: doctors, accountants (CPA, investment, or any financial related jobs), lawyers.
Secondly most Chinese believe in the old (outdated) method of "good beatings make good children" (棍头底下出孝子). Since that's how their parents discipline them, and they grow up to be alright, it must work for their children as well. I've seen people who're heavily disciplined as children themselves (a lot of these methods are pretty much child abuse) eagerly defend corporal punishment. "Because it works" or "They'll thank me when they're older" or even "I don't care if they hate me, as long as they get into Harvard".
And the media had played into this stereotype from the meme "Chinese father" to the book Battle Hymn of the Tiger Mother to all kinds of media depiction of strict Chinese parents and obedient socially awkward physically weak Chinese "A"s students...
Together you get this impression that many Chinese immigrants are tiger parents.