"Security improvements at the facility will be made and include the installation of additional CCTV cameras as well as extra lighting at the likely point of the man's alleged exit," Webb said.
Early indications suggested the man broke the security latch on the window to force his way out.
The man - who had been deported from Australia earlier this month - was swiftly taken into custody by police.
Police have reviewed a range of CCTV, interviewed the man, conducted a scene examination and spoken to staff.
However the investigation was ongoing and there were still some gaps about where he went during his overnight excursion.
The man was deported from Australia on September 16, and tested negative on day three and day 12 of his stay. He has not been charged at this stage.
Public Health deemed the Covid-19 risk to the public to be low.
"While this sort of incident is extremely frustrating, it is rare," Webb said.
Webb said anyone wilfully leaving the facilities would not be tolerated and that the appropriate action would be taken.
Of the 55,000 people who had been through managed isolation and quarantine - only 13 had absconded in nine different incidents.