The Puppets of Tomorrow are puppet forms of a few of the Legends who took over the Waverider in an alternate timeline. They were formed when Mick Rory became the Fairy Godmother's new host and called the Legends "Time Bureau puppets".
History
After they trapped Fairy Godmother due to John Constantine's actions, Mick Rory became her's new host and called the Legends "Time Bureau puppets", transforming them literally in puppets. Sometime after, Constantine enters the Waverider to see if the timeline is fixed, to which he find them and they starts to sing a music.