"It was a complete surprise for us," said Mackay, whose cousins have returned to their opera studies in Wales over the summer ahead of a national tour next year. "We had a little bit of feeling that maybe a few thousand albums might sell, just to people we'd met along the way, but to see it take off so fast, and on such a grand scale, really took us back."
Their name is a play on the Neapolitan standard O sole mio, the first thing they sang on stage together, while the 3 is for the trio and "sole" is Samoan slang for boy or brother.
Mackay said as of this year, every show had been a sell-out.
"I don't know what it is - I guess it's just us mucking around on the stage and enjoying what we do."
Unsurprisingly, Kiwi pop prodigy Lorde also enjoyed a strong year in the Kiwi charts.
The North Shore teen dominates the 2013 charts, taking out the No 2 and No 5 album spots for Pure Heroine and The Love Club EP respectively. She also claims the No 2 single for Royals.
Joining the ranks of leading Kiwi solo female artists is Los Angeles-based Ginny Blackmore, who grabbed a top spot on the singles chart this year with Bones.
The X Factor NZ winner Jackie Thomas also had her debut hit It's Worth It at No 1 on the singles chart for two weeks.
Last year's chart-topper, Adele, made the list again, breaking even more records. Her album 21 now holds the record for the most consecutive weeks on the chart, with 150.
How they charted: The Official NZ Music Charts
Top-selling albums of 2013
1. Sol3 Mio - Sol3 Mio
2. Pure Heroine - Lorde
3. Unorthodox Jukebox - Bruno Mars
4. The Truth About Love - Pink
5. The Love Club EP - Lorde
Top-selling New Zealand albums of 2013
1. Sol3 Mio - Sol3 Mio
2. Pure Heroine - Lorde
3. The Love Club EP - Lorde
4. Blackbird: Deluxe Edition - Fat Freddy's Drop
5. Delta - Shapeshifter
Top-selling singles of 2013
1. Blurred Lines - Robin Thicke featuring TI and Pharrell
2. Royals - Lorde
3. Just Give Me A Reason - Pink featuring Nate Ruess
4. Roar - Katy Perry
5. Impossible - James Arthur
Top-selling New Zealand singles of 2013
1. Royals - Lorde
2. Take It Easy - Stan Walker
3. Tennis Court - Lorde
4. Bones - Ginny Blackmore
5. It's Worth It - Jackie Thomas
Read more: New Zealand's top-selling music: The full list