The former Real Sociedad midfielder resisted attempts from Liverpool and Barcelona last summer.
"The first question I had to answer was whether I wanted to leave Real, and it wasn't the right time," he explained from Singapore when considering those offers from Liverpool and Barca.
"I felt that Real offered me more opportunities and that I still had a lot to learn, so staying at Real was the best decision for me."
On signing for Gunners manager Mikel Arteta, Zubimendi said: "I don't know what he saw in me, but I saw him as one of the top coaches in Europe.
"At the end of the day, I wanted a quality coach when I left Real Sociedad.
"I think I've found him. In the few days I've been here, I've seen how meticulous he is about every aspect of the game, so I think he's the one."
Zubimendi also says he is learning "a lot" from his new boss.
"I think I'm going to try to do things I didn't do before," he said. "Playing in that position, I'll try to bring balance and provide that passing outlet that I'm known for.
"Beyond that, I'm sure he'll ask me to do new things."
Time for trophies
Zubimendi is convinced Arsenal are capable of winning top silverware - if they get the "minor details" right.
He continued, "The most important thing about this club is that they learn from previous seasons.
"I think the lessons they've learned from how last season ended will be key to getting even closer to this year's targets.
"Ultimately, I believe that football comes down to details, especially in the Champions League.
"I feel that Arsenal were the only team in that semi-final who truly stood up to PSG, and they let it slip because of minor details.
"I also agree with Merino that it's a long season, and injuries play an important role, so the fewer we have, the better."