Epics by Rogue Shadows Coding is a stand-alone Power-Up. We do not store any data with a 3rd party server. All of the data collected & used by this Power-Up is stored within Trello itself and it is not sent anywhere else.
If reports are enabled on your board, then XML files (called snapshots) will be used to generate your reports. Snapshots are also generated from the board. Because snapshots aren't stored on any 3rd party server, you may need to store them locally or on your team's shared storage in order to generate reports. Snapshots contain some personal member information (namely, the member's display name and their Trello ID). Read more about reports & snapshots here.