The Irish winger felt like he had been rescued by the Catalan from exile at Spartak Moscow where he had been demoted to training with the youth players while he wound down his contract. His spell at Everton proved to be a false dawn, however, for a player who left Celtic for Russia in 2012 for what was, for the time, a massive £9m fee.
McGeady talks to Open Goal of how the smooth-talking Martinez persuaded him that his future with the Blues would be bright once he acclimatised to the Premier League but he was unable to ever hold down a regular place in two seasons during which the team as a whole was struggling for consistency itself.
"Everton didn't have to pay much for me, I was almost a free, and Spartak were buzzing to get rid of me because my contract was running out so they got some money," McGeady explains. "I thought, 'Everton are a really good club and I know Martinez likes me' — or I thought he liked me.
From that point on to the end of the season Martinez kept saying 'This six months is just to get you acclimatised to the Premier League' and I was kind of OK with it. I only started two games but I'd be coming off the bench. But that summer I went away and came back in really good nick, flying.
"I had a really good pre-season and then scored in the first game against Leicester and then the next game I was on the bench.
"That was the story of Everton for me. I just couldn't get going. I had the odd good game, I had the odd bad game when I was starting but I could never get a run of games.
"I was kind of always on the bench. I used to go in and see him and ask what was going on. I would rather he had just told me, 'I'm not having you'. But he would say 'Aiden you can be this, you can be that'. You'd go in thinking 'I will go in and say this' and he would absolutely Jedi mind-trick you. I'd come out and think, 'I didn't say the things I wanted to say'.
"He'd come and say 'How are you Aiden? How's things?"
"I just couldn't get going. It's a big club but I just couldn't get going. You're trying to impress but I only started three games in a row once.”
The beginning of the end at Everton for McGeady in terms of the first-team came at Barnsley early in the 2015-16 season in a League Cup tie at Barnsley where the team had to be rollicked by Martinez for a dreadful first-half display.
The winger was one of the targets of the manager's ire, along with the rest of the forward line, but he felt aggrieved at being the one sacrificed in the second half as Gerard Deulofeu sparked a revival that ended with the Blues winning 5-2.
McGeady has spoken of that evening being pivotal in his relationship with Martinez and it would be followed by months on the fringes of the team.
"He said the front four have been nothing short of a disgrace [at Barnsley] but then he took me off and left them on. They all scored in the second half and we won 5-2.
"I thought 'I've no chance now' and the next game I was completely left out of the squad for the first time in my career and after that I never got a look in.
"He would encourage me when I saw him but I said to him 'I need to be playing because I've got the Euros. I can't be not playing or I'll lose my place in the Ireland team'.
"But he'd said: "Aiden the last few weeks in training you've been unbelievable" and I'd say: "That's good am I going to get a chance?" and he'd say: "Keep doing it, keep doing it".
"He'd just repeat it next time."
McGeady appeared to be written off as a long-term prospect by Martinez's successor Ronald Koeman and he wasn't even assigned a squad number prior to the start of last season.
Now 30 and having spent a profitable season on loan under new Black Cats boss Simon Grayson at Preston last term having left behind the "egos", as he described them, in Everton's dressing room, McGeady has another chance at redemption on Wearside as Sunderland aim to bounce back into the top flight.