Like the title says , how or what, triggers Jyn's ability to place damage tokens on an Imperial controlled planet?

Hi,

It is the ability that is available to her from her character card. As it has the "Action" wording, it can be triggered during the action step of the players turn (when delivering cargo, bounties and purchasing from the market).

A player can carry out any number of different actions during the Action step, however each action can only be triggered/used once.

Hope this helps 😁