star trek - How exactly did the prisoners escape the Jem'hadar prisoner camp?

DS9 "By Inferno's Light":

MARTOK: He wired the message and the transmission coordinates directly
into the system circuitry. That way all he had to do was connect the
transmitter to the power grid and let it run.

WORF: Could the coordinates and the message be changed?

GARAK: You're planning to contact the runabout.

WORF: We could activate the transporter and beam ourselves onto the
ship.

BASHIR: And run like hell.

And then a bit later in the episode:

GARAK: Doctor, would you keep the noise down? I'm trying to work in
here.

BASHIR [OC]: Garak, how many translator circuits have you got left?

[Barracks]

GARAK [OC]: Three.

BASHIR: Well, work fast, because pretty soon we're going to be up to
our necks in Jem'Hadar.

Next scene:

KAT'IKA: I yield. I cannot defeat this Klingon. All I can do is kill
him, and that no longer holds my interest.

DEYOS: Shoot them both.

[Crawlspace]

GARAK: Got it.

[Internment centre]

(Just as Ikat'ika is killed, our heroes are beamed out.)

I loved the episode but was really confused by this aspect of it.

I don't understand how they escaped. They do not have communicators on. I assume there's gotta be some kind of shielding around the prison. There's a runabout floating in space close enough to transport that's unattended. Garek is being asked to send a coded message of some sort to the runabout to transport more people out then transported down, without communicators attached to them, in different areas.

What kind of message did Garek send to affect that kind of transport? How did a runabout sit close enough to the prison to be in transporter range, but not be detected? How did they flee Dominion space in a runabout without getting chased down after the transport?