"Spray-free" often just means swapping one spray for a gentler one, but there's a genuinely different approach available for tomato-potato psyllid specifically: physical exclusion. A 2015 New Zealand study tested mesh crop covers against TPP directly and found that mesh with pores under roughly 0.55mm on the shortest edge reliably stopped adult psyllids getting through to lay eggs on the plant at all. That's not pest control after the fact, it's simply not letting the problem start.
The practical setup is a lightweight mesh tunnel or cage over young tomato plants, secured at the ground so psyllids can't walk in underneath, from the day seedlings go in. This is the window that matters most: TPP is most damaging to young, actively growing plants, and a seedling protected through its first six to eight weeks has already avoided the period it's most vulnerable in.
The real limitation, and the reason mesh isn't a complete "set and forget" answer, is flowering. Tomatoes need insect pollination (or hand pollination) to set fruit, and mesh fine enough to exclude a psyllid also excludes bees. The realistic approach is mesh while the plant is establishing and before flowers open, then removing it once flowering starts, accepting a slightly higher exposure window in exchange for a plant that actually fruits. Hand-pollinating with a soft brush is the fallback if mesh needs to stay on longer, at the cost of a genuinely fiddly, time-consuming task most home gardeners would rather avoid.
On variety choice, it's worth being straightforwardly honest rather than repeating a claim that doesn't hold up: there is currently no scientifically confirmed, commercially available New Zealand tomato variety with proven psyllid resistance. Some research points to hairy-leaved varieties showing lower susceptibility, and there's real ongoing work breeding resistance traits in from wild tomato relatives, but none of that has reached a seed packet you can buy at a New Zealand garden centre yet. Anyone selling a specific variety as "psyllid-resistant" is currently getting ahead of the actual science.
there is currently no scientifically confirmed, commercially available New Zealand tomato variety with proven psyllid resistance
What does hold up, repeatedly, in both research and grower experience, is that psyllids disproportionately target plants that are already stressed, whether from inconsistent watering, poor soil, or being planted too early into cold, unsettled weather. A vigorous, well-grown plant isn't immune, but it's a measurably less attractive target than a struggling one, which makes basic growing conditions as much a part of a spray-free strategy as the mesh itself.
Combined, that's mesh through establishment, hand pollination or exposed flowering once the plant needs bees, and genuinely good growing conditions throughout, which together get a home gardener a long way toward a tomato crop that never needed a spray at all.