Dave Leadbeater, who was brought up in Brierley, had recommended Oakwell academy graduates Stones and Holgate to the Swans' hierarchy before they made moves to Premier League rivals Everton.
He said City were not going to miss out on a third Barnsley defender and were happy to outbid their rivals to secure Mawson's signature. He believes Mawson is good enough to go straight into Francesco Guidolin's first team and potentially replace former captain and Welsh international Ashley Williams.
"We liked Stones and Holgate but it's about what you need at the time," Leadbeater told the Chronicle.
"Back then we were not after a central defender but this time we were. "We lost Ashley and we wanted a homegrown lad to replace him. As soon as we heard other clubs were interested (in Mawson) we knocked the door down.
"He will play, he's not coming to make the numbers up. He's capable and I am sure he will be involved in our next game against Chelsea. He has got two decent feet, is powerful in both boxes and I am really glad we have got him."
Leadbeater, who previously worked at Middlesbrough under the likes of Gareth Southgate and Steve McLaren, hopes the Reds can cope with losing Mawson, who he says the club have had their eye on before he even signed for the Reds.
"It's hard for Barnsley because nobody wants to lose their best players. Barnsley have had a lot of success in the transfer market and they have got the price they wanted and they did not turn it into an auction. Everything was done above board.
"Barnsley have had a great start in the league and I'm sure they have enough to stay up because they will find replacements for the players they lose and they score a lot of goals. They've also got the right man in charge (head coach Paul Heckingbottom)."
Mawson's swift understanding of new leagues is what has impressed the scouts the most. After excelling in League Two with Wycombe, he was a virtual ever present in the Reds' promotion campaign from League One last season and had excelled in his first outings in the Championship.
"We knew about him at Wycombe on loan and what we noticed is how he has coped with every step up. He has really shot on at Barnsley. We have had scouts at all of his games and we wanted to see how he coped with the Championship.
"We were even going to watch him on Saturday if we hadn't agreed a fee by then. He scored two goals in his first few games. We think he can step up and there's no reason why he can't go all the way."