Residents directly next to Northam detention centre were not told of the latest escape involving two Vietnamese men on Friday night.
A probe into the actions of security firm Serco and the Department of Immigration will determine whether any recommendations were put in place after the first escape in August.
A Vietnamese asylum seeker was still on the run last night after escaping with a countryman from the Yongah Hill Immigration Detention Centre.
The men are believed to have scaled an internal fence and a perimeter fence.
Police recaptured one of the men in the Northam town centre about noon on Saturday.
Northam shire president Steven Pollard said he got a phone call from authorities about 10.30pm on Friday notifying him of the security breach. He said residents close to the centre were not told and he received a call on Saturday night from one of them asking what had happened.
Five Vietnamese detainees escaped from the centre in August.
All were eventually located, police finding the last man eight days after the escape.
A spokesman for Immigration Minister Scott Morrison said the detention services provider would investigate the circumstances of the escape.
Mr Pollard said the town's community reference group discussed their concerns with officials after the earlier breakout.
The group will meet again next month.
Of main concern is Serco's apparent lack of guards physically monitoring perimeter fences.
"We were told that was a result of what (Serco's) inquiries were following the August escape . . . We didn't see any official documents but we were told of the key findings and that increased staffing was highly recommended," Mr Pollard said.
"This is the second incident in four months.
"Are we going to have to go through this again?
"There needs to be some change, otherwise we will have to be dealing with this every few months. I don't think we can just keep going with an event that may occur every few months."