The left-of-centre Labour MSP refrained from endorsing publicly the Scottish Executive's collectively-agreed description of the fire strike as "unacceptable".
In two BBC interviews, she held back from endorsing the stance, prompting allegations from the Scottish National Party and the Tories that she had broken ranks with her colleagues.
But Mr McConnell retaliated: "I saw the interviews. It's a ridiculous exaggeration, typical of the personality rubbish we get in Scottish politics.
"It is time for everybody to grow up and talk about the issues rather than the personalities."
Members of the Scottish Executive are bound by the principle of "collective responsibility", meaning that once the ministers agree a position, each member must follow that line in public.
During the interviews, Ms Jamieson said it was important not to apportion blame and vital "to get things moving".
Scottish Conservative leader David McLetchie said Ms Jamieson was undermining the government's efforts to end the strike.
'One voice'
Speaking on BBC Radio Scotland, he said: "These people need to grow up.
"If they want the responsibilities of government they have to accept that part of the deal is the government has to speak with one voice.
"What we see with Cathy Jamieson, like Mike Watson on the Glasgow hospitals, is that they are trying to have the best of both worlds.
"You can't do that. If you want the perks, the profile and want to be a minister then you've got to take the responsibilities.
"Cathy Jamieson should grow up and realise that."
The SNP's Nicola Sturgeon said the minister had made her position untenable.
She said it was time for the minister to "make her mind up" if she supported the executive's stance on the strike.
Firefighters are staging an eight-day strike which is due to end at 0900 GMT on Saturday.
More strikes
Military crews have dealt with 2,840 emergencies including 44 in which lives could have been at risk. They also attended 24 road accidents.
Unless a deal can be reached the stoppage will be followed by two further eight-day walkouts next Wednesday and on 16 December.
Ricky Gray, of the Association of Chief Police Officers (ACPOS), said 2,140 emergency calls had been received from across Scotland relating to fires in the first week of the strike.
He said: "Of that number, the military have attended about 660. We believe that is fairly well down on what the fire brigade would normally be likely to attend."
Two teams of firefighters left their picket lines to assist military personnel deal with road accidents on Friday.
Discussing the dispute
One crew helped free a man from a car at Bellshill in Lanarkshire shortly before 1500 GMT on Friday, while a crew in Edinburgh used specialist equipment to release a woman trapped in a car following an accident on the A1 near the Newcraighall area of Edinburgh at about 1300 GMT.
The minister responsible for the fire service in Scotland resigned earlier this week after claims he described striking firefighters as "fascist bastards".
Deputy Justice Minister Richard Simpson admitted using the words when discussing the dispute.
However, he insisted he was only repeating what was being said by the public.