The head coach of the Welsh side, who replaced the outgoing Michael Laudrup, faces a manager who decided to "build a new squad" around the defender during his time in south Wales
The Everton manager recognised Monk's leadership qualities when he made the centre-back captain during his Swansea tenure.
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Swansea beat rivals Cardiff City 3-0 in Monk's first game in charge and he now turns his attention to an FA Cup fifth-round tie at Goodison Park on Sunday.
And Martinez is pleased to see Monk making an impressive start to his managerial career, though the Spaniard is determined to consign his former skipper to his first defeat this weekend.
He said: "The games are not about managers or where they have been.
"I'll always share magnificent memories of my time at Swansea but the game on Sunday is about the fifth round - a unique opportunity to get into the sixth round.
"Garry Monk was my first big decision as manager, I built a new squad around him. I knew he was the perfect captain.
"It's a nice twist, a nice moment to see him in the dugout on Sunday.
"The Welsh derby can be as intense as it gets for a new manager. It was a good start and he's showing that his group is reacting well. We expect a very difficult encounter on Sunday."
Martinez has fond memories of the FA Cup, having masterminded Wigan Athletic's shock triumph over Manchester City at Wembley in May.
Everton hammered League One strugglers Stevenage 4-0 in the fourth round, having thrashed Championship promotion-hopefuls QPR by the same scoreline in the previous round.
But he Merseyside club are still licking their wounds after suffering a 1-0 Premier League defeat at Tottenham last weekend - despite dominating much of the game.
Everton lacked a cutting edge at White Hart Lane without a recognised striker but Martinez revealed on Friday that January signing Lacina Traore is set to make his debut on Sunday either from the start or off the bench.
Romelu Lukaku [ankle] and Antolin Alcaraz [muscle fatigue] are not yet ready to return, while Bryan Oviedo [double leg fracture], Darron Gibson and Arouna Kone [both knee] are long-term absentees.
Capital One Cup holders Swansea secured 2-1 wins at Manchester United and Birmingham City to reach the fifth round and will be eyeing another away-day success this weekend.
Monk will check on the fitness of midfielder Jonjo Shelvey, who has missed the last two games with a hamstring problem. Michu, meanwhile, is closing in on a return from an ankle problem.