Does it mean "closely related with"?
"Natsuko Fujimaki, a Tokyo-based entrepreneur, says this is where the Japanese concept of majime comes into play. The term refers to a preference for order, tidiness, and often perfectionism. It tracks closely with a desire to stay reserved and sensible in comportment."
Source: http://www.businessinsider.com/japanese-students-hair-color-2017-5
Best Answer
Your guess is close, but "tracks closely with" also implies a relationship between the two concepts, in the sense that if someone possesses one they're likely to possess the other. I will use a simpler example to clarify this.
Not all people who are interested in computers are interested in programming. Not all people who are interested in programming are interested in computers. However, many people who are interested in computers are also interested in programming and vice versa. An interest in one usually implies interest in the other.
So to come back to the example given, it is saying that people who possess this sense of majime tend to also be reserved and sensible in their comportment.
I would like to add that this is not a very common phrase; as a native speaker it is one I have rarely come across in anything I've read or heard.