"I came in during that (tea) break and asked, 'When are we declaring?' and they said around 5.40," Warner revealed.
"So I kept on asking when we were out there. We got to 5pm, 5:10 and I was making sure that that was still the message.
"And it was until that last over before it just ticked over and Painey wanted me to try and get past that 334 mark.
"To achieve passing Sir Donald Bradman's highest Test score … It's something in the back of your mind you never think you're going to get yourself."
Taylor was in a broadcasting box on Saturday when Warner surpassed his record. He applauded Warner, saying he had no problem with the Aussie opener taking a chance to surpass 334 runs.
"Records are meant to be broken," Taylor said in commentary for Macquarie Sports Radio.
"I got to 334 with two balls to go on the second night of that game. And I tried to hit them as David did.
"I tried to hit them for runs and they both were fielded. One was really well fielded by Ijaz Ahmed, who stopped me from going past Bradman's score.
"And if it did go past him, I would have taken the runs.
"And I would have ended up on 335 because the game is not about individual records. The game is about winning and losing."
"100 per cent I was aware of it," Warner said. "You grow up knowing what those milestones are.
"You look at the history books and say, 'How did they get there?' It's a long time in the middle. It takes a lot of patience, which I surprised myself.
"Around 280. I wasn't teary, but I was thinking, 'This could actually happen'," Warner said in an interview on Fox Sports.
When he reached 300, the TV cameras panned onto his wife, Candice, wiping away tears from behind her sunglasses. It's been an emotional ride for Warner, his wife and their three daughters.
Candice, who has stood by Warner as he went through hell after the ball tampering scandal, posted an emotional message on Instagram to celebrate her husband's record-breaking day.
Bradman's 334 wasn't the only mark Warner bettered, as his triple century overtook The Don's record of 299 not out as the highest Test score at the Adelaide Oval. In a tough day for the country's greatest ever batsman, Steve Smith also surpassed his mark of 6996 runs to go down to 12th on the all-time Australian list.
Warner hit 39 boundaries and one six and 80 of his runs came from cover drives as he ran hard throughout.
He passed his previous best mark of 253 just before tea and looked to the sky as he reached both 200 and 300 on what would have been Phillip Hughes' 31st birthday.
"I will cherish this moment for the rest of my life," Warner said. "It sunk into me it's very rare you get these opportunities. There was so much time to go in the game.
"There were 70 overs to go in the day and I was on 270. You think this is a chance I'm probably never going to get (to reach 300)."
Meanwhile Warner would still likely have needed close to another hour to challenge Lara's mark, taking Australia towards the dinner break.
No doubt front and centre of Paine's mind was rain forecast over the remaining days, and the 60 points on offer for a win in the World Test Championship. Warner though insisted it was the right one, as Australia's bowlers made use of the extra overs before stumps to leave Pakistan reeling at 6/96.
"We really looked at the weather that is around (on Sunday)," Warner said. "It wasn't a thing in our mind to go out there and try and get that record. It was more about putting our team in a great position to try and win the Test.
"If there is a bit of rain about tomorrow the bowlers get a good rest, then you only have to get 14 wickets in the last two days."
