Taylor, 32, penned a one-year deal with Wellington in July having made more than 250 appearances for the Magpies, including almost 200 in the Premier League.
The ex-England youth international left Newcastle in 2016, before spells with Portland Timbers in the United States, along with English clubs Ipswich and Peterborough.
Taylor made 51 appearances for League One outfit Peterborough last season but was transfer listed along with a dozen others after missing promotion.
The central defender was contacted by Phoenix, among several other clubs, and was lured by the challenge of reviving a club who’ve missed the finals the past three years, casting uncertainty on their future with their licence due to expire in 2020.
“It must have happened two weeks before I came out here,” Taylor told FourFourTwo. “There was contact with the manager (Mark Rudan) and my agent. He mentioned the opportunity.
“There were a few other things in Europe but there wasn’t anything which had this sort of challenge ahead.
“They were midtable options and they didn’t want to move forward.”
Taylor said he has been impressed by the Phoenix staff and coach Mark Rudan, who is demanding higher standards.
The Englishman called on his teammates to embrace the challenge of responding to the critics who’ve suggested the club should be axed from the A-League and wrote them off as contenders.
“I hear a lot of media writing Wellington off and that’s something the lads have got to deal with,” he said. “We’ve got to step up and feel the excitement more than anything.
“We’ve got good characters in the dressing room and young boys taking on the responsibility. You’ve got hungry players here now which is very important.”
Taylor also said Australia and New Zealand sporting organisations had a great professional reputation which was a factor behind his move.
He added: “This was an opportunity to come somewhere with top-notch sports science and facilities.
“You’ve only got to look at the behind the scenes here. New Zealand and Australia are well thought of for sports science.
“I’ve seen a lot of games back home in England on Sky Sports. I know there’s only 27 games out here, but every game is going to be a difficult one.”