Question on Final Fantasy 13's plot
It is unclear if the Sactum actually know that they were branded and Pulse L'cie, but according to Purge wiki, PSICOM was sent into to hunt them down regardless and apprehend them
I'm rephrasing the content from the wiki to avoid spoilers
After Lightning, Snow, Sazh, Vanille, and Hope have been turned into Pulse l'Cie, PSICOM is dispatched to hunt down them and the other Purge survivors
Actual content
After Lightning, Snow, Sazh, and Hope have been turned into Pulse l'Cie, PSICOM is dispatched to hunt down them, Vanille, and the other Purge survivors.
In the section when Snow is attack by PSICOM they locate Snow and say
L'cie spotted ..... Pusle L'cie confirmed.
We can see this in this Youtube video
This quote can be understood that they have a general idea they were L'cie, but required confirmation.