The details of this setup are not explained, but left for the viewer to piece together.
What is apparent is that both 'Jon' and 'Anna' (Azure) are aware that they are living in hiding of something. Both seem to be aware of what the beeping of the warning device means. When they see the mini flying saucer in their garage, neither seem surprised by the alien tech. They both understand who is sending the message.
JON: What do we do?
ANNA: I don't know.
JON: Can we ignore it?
ANNA: They promised this would never happen.
JON: Except in the gravest of emergencies.
Later, when Swarm arrives, 'Anna' seems to have her previous memories and identity restored, just before she turns back into Azure:
ANNA: Why is this thought in my mind?
SWARM: What thought?
ANNA: Thank you.
We know that Swarm was imprisoned by Division, so it is logical to conclude that Azure was hidden on Earth by Division, also. The arrangement of Azure living on Earth as a human with her memories erased and with a companion is so strikingly similar to the situation where the Fugitive Doctor was hiding from Division under the identity 'Ruth Clayton' that it also seems logical to believe that other details may be similar too - that perhaps Azure had her memory and personality (and physical appearance) replaced to conceal her identity, but perhaps her companion was more aware of the truth and assigned to protect her. Although The Fugitive Doctor was hiding from Division while Azure was hidden by them, we do know that both The Doctor and Lee Clayton had Division training so may have employed similar methods in hiding.