Does "when I'm played" trigger when LeBlanc plays her Reflection on a Harness Dragon?

No. The Reflection token created by LeBlanc's Deceiver legend does not trigger the "When you play me" ability, even if it copies Harnessed Dragon.

There are two reasons. First, the Reflection token is created by Deceiver's ability, not played from your hand — the "play" in Deceiver's text is a token creation effect, not the act of playing a card from hand. Second, the copy effect happens after the token resolves, so the token never has Harnessed Dragon's "When you play me" text at the moment it enters play — that ability is gained later via copying and can't retroactively trigger (FAQ #10386).