First of all, I am answering this question from my own point of view. My opinion may not represent the majority of Asians (although I am an Asian myself).
I think one of the reasons your school invited you to teach there is for internationalization and diversification besides your excellent academic credentials. They would like to have not only your expert knowledge but also the views you can bring to them.
@UV-D gave an excellent answer. The strange blinking pattern could be a medical issue, so you need to take it to somebody else’s attention. I think he is right. However, as you noticed, you need to take care of the issue carefully.
Fairness and consistency would be the keys. Suppose you are a male professor and the student happens to be a female, there is a possibility this could become a gossip, something like “Our teacher likes that girl”. The gossip would spread until the next time you do the same or similar thing to a male student. Everybody would then say “Ah, he is just a very nice teacher, take care of everybody”.
I think people (not only Asians) would like to be treated fairly. Consistent actions between multiple events will make people think you are being fair. So, my point is, you’ll be fine as long as you keep your actions fair and consistent and do whatever you think is right.
An important note. Be extremely careful when dealing with the students outside the classroom. I noticed in your question, pull that student aside. This could potentially become a harassment case. Talk to an authority may be a better way to handle it. A western white lecturer in an Asian university is always the focus of the students and the faculty.