"And there are some songs such as Loco Mama, which I wrote before my Dad died, so it's not all doom and gloom," she laughs.
The Canadian has made a home in New Zealand for the past 10 years and has been roundly welcomed here, winning the Best Country Album Tui four times (2009, 2010, 2012, 2015), as well as the Silver Scroll, and being nominated for the Taite Prize for her last album Dynamite!, which received five-star reviews and was on The Guardian's Top 10 Country Albums of 2014 list.
Perhaps that's not a surprising ascent for someone who's been singing and performing her whole life, someone whose family toured North America for 10 years, opening for the likes of Johnny Cash.
Her family have remained tight-knit in their music-making despite being on opposite sides of the Pacific, so when Neilson's father Ron became suddenly and seriously ill in February, she raced to Canada to be by his bedside.
His subsequent passing left an enormous gap in her life, both musical and personal. But it turned out music was one thing that helped to pull her through.
"I had this studio time booked for April, and my first reaction was 'I'm cancelling it'. I just couldn't see it happening, specially with two little ones [Neilson has a 3-year-old son and 1-year-old son with her Kiwi husband], and barely just getting through the day, let alone putting out anything creative. But I think that the moment it really switched and clicked for me, was when Mum said: 'Dad left all his demos on the computer, why don't you have a look at them, maybe they can help you.'"
The fact that her father had also been writing a song in his final days in hospital spurred her on too.
"One of my promises to Dad, when we were losing him, I said to him, 'Dad don't worry, I'm going to keep your music alive, and I'll be your lungs'.
"He had this song he was writing, Don't Be Afraid, and he couldn't sing it because he was on oxygen, but there's nothing worse for a songwriter than having a song in your head and not being able to put it down, so I said to him, 'I'll bring in your guitar, and we'll work on it'.
"And every person that came to the hospital to visit, he would show them the lyrics, and tell them about it. And for him to be so enthusiastic about that song, it seemed like it was something that was really important for him to leave behind. So after he died, my brother, Jay, and I decided, let's finish this song."
That was the first song they finished, and the huge, powerful, spine-tingling blues ballad turned out to be the first song for the album. Tami and Jay then turned to Ron's demos, and found further inspiration.
"I think once I'd gotten to that point of finishing the songs that Dad had started, for me all of a sudden it became a real mission. And it felt like it was something that could actually help me to process my grief, and to feel like I was doing something productive. So it was a healing process for me."
Another key inspiration for her during this time was Mavis Staples. Neilson had long been a fan, and found solace not just in her music, but in the connection she felt with Mavis' life - a soul singer who'd grown up on stage, singing with her family, who lost her father, and found some closure in bringing his music back to life.
"I was listening to her album, One True Vine, a lot during the drives back and forth to the hospital, so that was my soundtrack of that time in a way. And I'd also been excited for months about the fact that Pops Staples' posthumous album was coming out - the one Mavis had kind of handed over to Jeff Tweedy and asked if he could produce. And I'd talked to Dad about it, and we were both excited."
Neilson knew the album was due out in Canada on February 17 and tried to track it down in record stores to no avail, so eventually ordered the vinyl online.
"It arrived the day after he died," she smiles wryly. "And when you're in that grief, you know, I'd totally forgotten about it, but then his parcel arrived, and I opened it, and I just sobbed, because here it was, this album that had been treasured and kept safe by his daughter, and years later she's brought it to life, and it was out there for the world to enjoy, and celebrate him. And so I think that was a huge influence even subconsciously."
Part of what made Dynamite! special was the team around her - producer, co-writer, and guitarist Delaney Davidson, co-producer and engineer Ben Edwards, her band Dave Khan, Ben Woolley and Joe McCallum ("my boys" she calls them) - and it was their support and understanding of this project that helped her to finish it.
"They were so important in me moving forward. It's all down to having them around to support me - that means I'm able to do what I do.
"Also I think you bring the best of the best that you can possibly bring to the table when you're working with people you really respect and admire. You get the best quality of work from everybody, and so even though Don't Be Afraid is very different to Dynamite! in its content, I think the fact it's the same family of players, and same styles that those boys bring to the album, means we're still painting with the same palette."
Along with writing and recording an album, Neilson also got back on that performance horse, playing shows around New Zealand.
"I started dipping my toes in the water, performing a song here or there to see how I would handle it. The more I played those songs, the more people would come and talk to me about how they were going through a divorce, or had someone pass away, or all sorts of different things, and I realised that everyone can relate to that emotion of losing someone or even something, whether through death or other circumstances, so it's not specifically just about a daughter losing her father."
Neilson also managed to score the entire soundtrack for the upcoming series of The Brokenwood Mysteries, collaborating with brother Jay. "It's been a huge learning curve, but an amazing experience, and very exciting to hear music Jay and I created coming to life, as part of a story."
Shortly she'll be heading off across New Zealand as part of the annual Church Tour, alongside her friends Delaney Davidson and Marlon Williams, with new tour mate Barry Saunders.
Tami Neilson really is a force to be reckoned with.
Who: Tami Neilson
What: New album Don't Be Afraid
Where and when: Don't Be Afraid is being released with a special show at The Tuning Fork on Friday September 25. Neilson is also touring the country as part of the Lost Highway Church Tour, along with Marlon Williams, Delaney Davidson, and Barry Saunders. They perform two dates in Auckland at the Holy Trinity Cathedral on Saturday October 3, and St Mary's Church on Sunday October 4.
