Yes, part of it
Tongue of the Sun and Moon is two features under one ability name. You have the ability to understand all spoken languages, and other creatures are capable of understanding your speech. If you want to choose to NOT understand a creature's speech, you are allowed to not understand.
The way I see it, the second sentence can be interpreted in two ways: 1) "Any creature that is capable of understanding a language is capable of understanding what you say, end of story," and 2) "Any creature that is capable of understanding a language may choose to understand what you say." Whichever interpretation of the wording the GM goes with, it is not the monk's choice whether other creatures are able to understand him.