Although Villa have greater history, resources and support, Martinez opted to continue the job he started two years ago at the DW Stadium.
Wigan's stadium is named after their chairman, who was happy not only to stick with Martinez last season but for the Spaniard to keep urging his side to play passing football.
The Latics, who travel to Villa Park on Saturday, ultimately escaped relegation on the final day and Martinez, 38, hailed Whelan for backing him when others would have lost faith.
"I want to play in a certain way and not many people understand that," he said.
"We were flirting with relegation and were in the bottom three.
"Many other chairmen would have changed direction in the way we play and got a different manager. I understand that is what happens.
"But he [Whelan] said that whatever happened there was a three-year plan to do what I wanted to do. That is why I wanted to repay his support. I didn't think the time was right for Wigan to have a change of manager."
Martinez admitted that joining Villa was a big possibility after they made an official approach, but it only took a simple answer from Whelan to convince him to stay.
"I had a meeting with the chairman at the ground," he said. "I went in with an open mind, I wanted to know what the chairman wanted to do. The moment he wanted me to stay, the conversation was ended.
"I have got a strong belief in what I want to do to progress to the next level. The chairman agreed, so we just carried on working as normal.
"It wasn't about the other football club or the other job. It was about the relationship with my chairman.
"Some don't have patience with their managers and their projects. But he had always been incredibly supportive.
"I can't speak about other chairmen, I don't know them. But our chairman is the reason why Wigan are in the Premier League. He is unique, he is successful but also honest and straight.
"He tells you how he sees it, you know where you are with him. We have got our limitations - as everyone does - but he lets me do my work and do my job. That is something I don't take for granted in modern football."