'My mum is from Cardiff,' he said. 'She still has a Welsh accent. And my grandparents – who have passed away now – were both born and bred in Wales. I know there are always arguments about time service and things like that, and I was crucified for that when I first came over here.
'It was frustrating to deal with, because it's not like we had to find some great, great grandparent who we didn't know. My mother was born and bred in Wales, my grandparents were Welsh and I've got a lot of second cousins still living in Wales. I don't know if I'm 50-50 Welsh-Kiwi – but I used to have a jersey that was half red for Wales and half black for New Zealand.
'I've made a real effort. When Hadleigh Parkes (the Scarlets' Kiwi centre) made his debut for Wales, he sang the national anthem. We made efforts to learn the anthem and I feel that shows we are connected to the place. It's not an easy anthem to learn, I can tell you! I wanted to do that.
'I've been here almost four years now and hopefully people are starting to think of me as Welsh. Every now and then people will still say, 'You're a Kiwi' and I don't want to take away my New Zealand heritage, but that (being seen as Welsh) has taken time and it will continue to take time.'
That is just one part of the struggle for acceptance. It has been a tortuous process at times. 'The good thing in Wales is that people are passionate about rugby, but on the other side of it, everyone has an opinion,' he said. 'Part of me maturing has been learning to deal with that stuff; accepting the good and the bad, and not get fixated on things.
'You're not going to please everyone. For some reason, my name has managed to rile up a lot of people in Wales and I'm not too sure why. Maybe it's because it (move to Wales from New Zealand) got built up a lot, or my connection to Gats, for some reason. Maybe that annoyed people. I just seem to be someone who has riled people up. I've learned to not get caught up in it.
'At the start, when I was first over, my family struggled with it all, but you've just got to take things with a grain of salt at times. I feel a lot more at ease now. And hopefully, slowly, I have changed the public's perception of me. It feels as though people are accepting me more.'
Anscombe deserves his acceptance. He is a friendly, engaging and very likeable character. He speaks openly and honestly about how he and his Serbia-born fiancée, Milica ('pronounced Melissa') took time to settle in Cardiff. It wasn't just about the weather, but that was part of it.
Milica works for a radio station in Cardiff Bay and the couple live just to the west of the city. Having established a social network, it now feels like home. The exiled New Zealanders keep in touch. 'We have a Kiwi crew who meet up every couple of weeks for some food,' said Anscombe – talking exclusively to Sportsmail ahead of the Blues' sold-out home clash with Glasgow in the Heineken Champions Cup on Sunday. 'Then we get together for an "orphan Christmas" every year – and try to have a barbecue in the snow!'
So many team-mates from his time in the New Zealand Under 20 side are now playing on this side of the world; from Lima Sopoaga and Brad Shields – now an England player – at Wasps, to Steven Luatua and Charles Piutau at Bristol. That 'Baby Blacks' class of 2011 beat England in the final and also contained current Kiwi icons such as Beauden Barrett and Brodie Retallick. Anscombe was the first-choice fly-half, Barrett operated at full-back. 'It was one hell of a team,' he said. Indeed.
In those days, he dreamed of wearing the black No 10 shirt. Now he has his eyes on the same prize, but in red. Since his round-the-world transfer in 2014, Anscombe has become well aware of the Welsh obsession with that particular area of selection. He's ready to embrace being in the eye of that storm of speculation and intrigue.
'Playing at 10, you get a lot of attention – a lot of the spotlight on you,' he said. 'In Wales, the No 10 jersey has a famous history. I was always aware of that coming over. It's always been a glamour position, and Wales have often had superstars in that position. You live and die by the sword in that position and that's part of the job.
'I'm glad to be in those conversations within Wales now, about the No 10 jersey. I'd love to get the chance to play with that jersey on my back. Hopefully I can play well over the next six to 12 months and take my opportunities.'
The plan is for Anscombe and Milica to get married in June, back in New Zealand. They will finalise arrangements once he knows all the details of Wales' pre-World Cup training camps. Life and career landmarks are looming in front of him. 'Hopefully 2019 turns out to be a good year,' he said.
And what of Welsh prospects? 'We feel like we're building really nicely for the Six Nations and the World Cup – and that we might come in under the radar a little bit, which suits us just fine.'
Anscombe himself has never been under the radar, since he left Waikato. But the glare has become more bearable of late. That's what comes with acceptance.