In a comment to one of the other answers, you said that he is "a man with lovely feelings that he keeps private."
It seems to me that private would work well:
[Merriam-Webster]
3 a : withdrawn from company or observation
// a private retreat
b : not known or intended to be known publicly : SECRET
c : preferring to keep personal affairs to oneself : valuing privacy highly
So:
In general, he is private.
Or:
In general, he is a private person.
I qualified this with in general because, as you said, he doesn't always keep things to himself, and not with everyone.
You could also say that it's his sense of privacy that keeps his emotions hidden from other people.
In terms of your example sentence, if you're looking for a quality that actively enables him to keep his emotions to himself, I would say:
His self-composed nature enabled him to hide his strong emotions from others.
Merriam-Webster defines self-composed as:
: having control over one's emotions : CALM