The 30-year-old was already in Australia, playing for Sydney Thunder in the Big Bash League.
Billings revealed that he was two hours away from a flight home when he was asked about the possibility of linking up with the England Test team.
He said: "It's been a bit of a rollercoaster. I was probably 90 minutes to two hours away from getting on that plane back to the UK. It all happened pretty quickly.
"I went to the airport, got the rental car and cracked on, basically. It's been a bit of a whirlwind. For the first 24 hours I hadn't heard anything or seen anyone, I'm sure I'll find out later this week if I'm playing.
"I'm just really looking forward to it. Like any side I go into, I will try to make a positive impact on and off the field, and add to any environment I am put into. We will have to wait and see if that Test cap does come."
Wicketkeeper Jos Buttler is ruled out ahead of next week's Ashes finale due to a fractured finger while Jonny Bairstow is currently carrying a thumb injury. With that in mind, Billings appears to be in prime position to step in and make a name for himself in what has been a dreadful series for the tourists.
Despite the drastic change of format, he is feeling excited about the opportunity of making his debut for the England Test team.
He said: "Regardless of the format, regardless of circumstances, with experience and maturity you can get a sense of where your game is at.
"I've been playing and scoring runs. I'm 100 per cent ready if required. It doesn't really matter what format it is, it's more about rhythm, confidence and mindset. As a player you look where your opportunities may lie to progress your career…for me it has always been with the white-ball side so far.
"But this has been on the radar, it's something I've really wanted to do."
Billings did have to ponder his position when he was invited to join up as injury cover.
He was already in the Twenty20 squad that will play a three-match series against the West Indies later this month and, with Covid restrictions around travel, he was eager not to sacrifice that opportunity for a 12th man role in Tasmania.
He added: "I had a few moments on my own in my hotel room and weighed it up, of course. I've done way too much running the drinks.
"I just need to play cricket. I wasn't going to compromise that opportunity in the West Indies but of course I will always help and offer anything I can to the England team.
"I think I got that assurance that I would make it to the West Indies as well, whether I got the opportunity or not."