The Strathkelvin and Bearsden MSP questioned officials from East Dunbartonshire Council on Thursday night at Bearsden Hub.
Save the Children also held a presentation revealing the circumstances facing refugees fleeing Syria.
Officials in charge revealed it would take around two weeks to process the case load from the Home Office and then another six to eight weeks for the refugees to arrive.
Families will be housed by a mixture of housing association and council stock in the area. However, the four child refugees – aged between 12 and 18 – will be settled in a care facility with 24-hour staffing, with a view of homing them with families in the future.
Ms Mackay said: “The attendance of the meeting in Bearsden Hub mirrors the overwhelming support the people here have for helping people fleeing war in Syria. There is a lot of compassion and enthusiasm for helping the integration process.
“What was also clear from the meeting is the will the attendees had for resettling more families making the dreadful exodus from Syria.
“Obviously, there are concerns with housing stock in the area but I hope the new council can move on with a view of extending this resettlement programme like many other local authorities in Scotland have done.
“While the enthusiasm is welcomed, I want to echo views of the council and public that we cannot overwhelm the families and young people coming here – because what they have been forced to go through is nightmarish. We must respect their privacy and vulnerability as they enter this new environment.
“I would like to thank the council for arranging this meeting and for the work they have done so far in helping the people coming here, it was very powerful to hear from Save the Children.”