herald, announce, follow, obey, seek, lay down one's life
徇 centers on public declaration and self-sacrificing commitment: heralding or announcing something widely, and following through even to the point of laying down one's life. The obey and seek senses are natural extensions of this devoted, declarative action.
徇 combines 彳 (movement, going) with 旬, which likely contributes the sound. The character is associated with proclaiming or making something known widely, and by extension, following or sacrificing oneself for a cause.
A person (彳) moving through a ten-day period (旬) to announce a message everywhere, even at the cost of their life. The dedication to spreading the word captures both the herald and self-sacrifice meanings.
For ジュン, imagine a herald in June announcing a decree: June -> ジュン, and the herald follows the order without question.