It’s an interesting case. Tuatara appear to have very slow metabolisms and long lives (perhaps averaging about 60 years, with one male documented as reproducing at 111 years old). They also reproduce slowly: “females mate and lay eggs once every four years”.
Tuatara were released into the Zealandia sanctuary in 2005 and nests and hatchlings were documented within 3–4 years, so certainly some individuals seen now were born there. Also, as others have said, the population is apparently not cared for, except for the maintenance of the exclusion fence.
I would guess that many of the observations on iNaturalist are members of the founding population and some were individuals born in the sanctuary over the past 20 years. The two human actions that might justify a “captive” designation are the translocation of the founding population and the continued maintenance of the fence. Set against that, these are wild animals living wild lives in part of their original range. I feel that justifies treating them as wild for iNat’s purposes.