Thanks very much Maisa. I hope I'm not getting myself paranoid. I wouldn't worry about this a few weeks ago, but I started reading discussions here. I saw people who live in Canada got RQ just because they travel to US a couple times.
I got my PhD one year ago after studying in Canada since 2008, and landed as a PR 5 months ago. Now one of my co-supervisors in US offers to hire me as a research consultant. My supervisor is ok with me not going to US to work, because he understands how much I want to get a Canadian passport. He's looking for ways to pay me here, and I don't want his effort to be wasted if my US income will become a problem in the future.
Theoretically a person who lived 1095 days out of past 4 years will get his citizenship, but it's getting harder these days. I hope my situation won't be a catch-22. I'll very much appreciate if anyone with similar experience can put my mind to ease, so that I can let my supervisor know the US payment won't be a problem in the future. Thanks!