As the Doctor told Kate Stewart, Missy (the Master) had been running the operation for a very long time:

DOCTOR: Dead bodies don't have minds, of course, but she's been upgrading dying minds to a hard drive for a long time. So she upgrades the hardware, and then she updates the software.
KATE: What do you mean, a long time? How long?
DOCTOR: Well, she must have a TARDIS somewhere, so as long as she likes. The past, the future.[1]

Given time-travel capability, Missy could have uploaded the dying from any era she wanted. She was definitely using Time Lord technology. The Time Lords have more methods of time travel than just TARDISes, of course,[2] although (as the Doctor indicated) a TARDIS is the most likely.

  1. From "Death in Heaven", transcript here.
  2. The Time Lords have used time rings, for example, as shown in "Genesis of the Daleks" & "Revenge of the Cybermen".