The word "suit" as a verb means "to meet the requirements of" or "to be appropriate for". It is a straightforward use of the dictionary definition to say, "Your comment describes Bob perfectly. What you said suits him very well."
We commonly say that something "fits X to a tee", meaning that it fits him very well. You can say this in a literal sense, like, "that shirt fits Bob to a tee", or in a more figurative sense, "Bob's new job is exactly the kind of job he wanted. The job fits him to a tee."
"It's him to a tee" is a short-hand version of this.
Both are common and "natural", yes.