The Citizens head into the return fixture with a 3-1 advantage after winning the first leg at Moses Mabhida Stadium last weekend.
However, Tinkler was critical of his side’s approach, suggesting they had taken the encounter for granted at times.
The coach believes addressing that mindset will be crucial if Durban City are to progress and become a competitive force in the group stages.
"We've got to turn them not into tourists but into locals; it's as simple as that. Do we want to be tourists, or do we want to be locals? Because a tourist means you're here for one or two weeks and then you go home. We don't want to be tourists – we want to be locals. It's the same with the CAF competition – I don't want to be a tourist in the CAF competition, I want to be a local. That's got to be the mindset. You've got to set your targets and objectives high," said Tinkler.
Experienced on the continent having previously been in this competition with both Orlando Pirates and SuperSport United, Tinkler insisted that City’s quality will trump any unforeseen circumstance – especially on the road.
Meanwhile, AS Port Louis coach Clarel Beeharry is confident they can claw their way back in Mauritius playing on their own turf.
"Yes, it is very difficult to get a goal in the last minute, as the score was 2-1, so the team was trying to look for at least a draw. There was also an error, as we had two coaches who weren't on the bench. Issues were raised regarding their names; they were marked incorrectly, so those were some of the issues we could not control."
Beeharry added that their preparation will be a lot better this time around having had some logistical challenges when they were travelling to SA.