"It was all a bit of a whirlwind," says Eugene. "It was really accidental rather than by design. We went from obscurity to being very well known."
One minute they were sitting in confession, listening to the troubles of rural parishioners in Northern Ireland. The next they were collecting gold and platinum discs.
One minute they were making their way to isolated farms to meet members of their local community, the next they were being flown to St Peter's Basilica, to record at The Vatican.
"I think someone must have lent a helping hand to make that happen," adds Eugene.
"If we"d sent a formal request we might still be waiting for a response now. St Peter"s Basilica is so spectacular and it isn't easy to organise things like that."
David says: "We were very busy the first couple of years, recording and releasing those albums.
"The albums were released internationally which meant there was a lot of travel, which took us around the world. It was all very exciting.
"Sony invested a lot of money in the project and they were giving us the full celebrity treatment with lots of nice hotels. It was very interesting and pleasant but very demanding and tiring as well.
"We were trying to make sure all our duties in the parish were covered. After three albums, we decided it was time to reduce our travelling and spend more time in our parishes."
The Priests will be back on 9th October 2016 with their fourth studio album.
Martin says: "We didn't expect that level of success at all. It was somewhat meteoric. It developed over a very short and intense period of time. Sony initially approached us and offered us a contract for the UK and Ireland.
Then they decided to go global. It was a global priority. We were absolutely flummoxed and delighted and intrigued. It"s safe to say, we were not your average boy band."
The Priests have found a happy medium, where they are able to balance the responsibilities of parish life with maintaining a global career.
By co-ordinating their diaries, seeking the support of colleagues and devoting their energies to their music, they remain at the forefront of religious and secular music.
The classical music trio have more ideas in the pipeline and hope that the release of their fourth album will be followed by a feature film, called Raising the Roof.
The movie is currently in pre-production in Hollywood and could give them the opportunity to enjoy a red carpet premiere.