Residents face a ban on entering “sensitive areas” of the town, including the vicinity of schools and public swimming pools.
Centre-left politicians and human rights groups say such a ban is not lawful and cannot be enforced.
The provisional centre – a former military barracks – is the first to open since Swiss voters approached tougher asylum laws in June.
It will house up to 150 asylum seekers over a three-year period. The first 23 people moved in on Monday.
The first group was made up of men, women and two children from Eritrea, Tibet, Sri Lanka and Sudan, the Tages-Anzeiger newspaper reported.
The Federal Office of Migration said the ban on asylum applicants entering certain areas of the town had been agreed with the Bremgarten authorities.
The Tages-Anzeiger reported that it had now revised its earlier announcement and was saying that there was no formal ban.
It quoted Urs von Däniken of the Migration Office as saying instead that there were “sensitive zones, which asylum seekers should not enter”.
“These zones were defined in the interests of a good co-existence between the population and asylum seekers,” von Däniken said.
Apart from schools and swimming pools these include old people’s homes and homes for the disabled.
“If someone goes to the pool and nothing happens they won’t face any sanctions,” the Migration Office official said, quoted by the paper.
“But if an asylum seeker behaves badly or poses a threat to public order he can be served a ban on going out or entering certain areas.”
Human rights group Augenauf condemned the move saying the Migration Office was calculating that the centre residents would not enter the areas defined out of fear of the consequences.