Taylor is getting ready for his first competitive game in charge of the Saddlers, having taking over earlier this summer, at Tranmere on Saturday.
Working with Fullarton, the pair have brought in 12 new players going into the new League Two campaign. And Taylor says that dynamic was a key factor in leaving his role as a youth coach at Tottenham for Walsall.
"I first had a conversation with Jamie four to six weeks before anything was agreed," said Taylor during a Q&A with fans at the Banks's Stadium.
"I was very open and transparent over the situation with Tottenham, and I met Jamie and had a conversation for around two and a half hours.
"He spoke about where, alongside the chairman, he wanted the football club to go and the vision.
"We spoke in depth about my philosophy and how I saw myself moving forward as a coach, and I knew pretty instantly that my core values were matched by the chairman (Leigh Pomlett), Jamie and Stefan (Gamble, chief executive).
"It was about whether I could work alongside these people, and the simple answer was yes.
"From a personal point of view, I was in a job where I was extremely happy and challenged on a daily basis.
"And to be brutally honest, I asked myself the question whether I was ready.
"But my mindset has changed now, and it's a really good fit.
"I'm extremely proud to be the head coach and likewise, I probably wouldn't have taken the job if it wasn't for Jamie.
"I don't want to be, and I'm not, the old-school archetypal manager that controls everything at the club.
"My focus is on the grass with the players, and we definitely wouldn't have got the players over the line we have done if it wasn't for Jamie being so tenacious and myself going in the car to meet players."
Tyrese Shade became the latest signing earlier this week on a season-long loan from Leicester.
Walsall are also on the lookout for another attacker.
On the recruitment process, Taylor added: "It's a two or three-pronged approach to make sure we have the right individual.
"The player for me is second, they have to be the right type of person.
"So, all I can say is it's a really good fit and I'm extremely happy with how it's gone so far."