The codebreaker already ratted them out though. They were ratted out before they got to the tracking room
They were ratted out for trying to disable the tracker to jump without being noticed. They were not aware of the cloaked shuttles heading to the outpost until that communication. Without that interference the shuttle fleet would have got away.
Poe's plan was horribly flawed from the beginning. He took it upon himself to go behind the back of the commanders and set them up to die without knowing they would have been safe.
Holdo was completely right to not give Poe information. He shared it freely when he did get it and endangered everyone. ---