(I'll call them Diplodium in responding to this as it's so much easier)
It depends on the normal flowering time for the species you're growing. Diplodium will flower from summer to winter depending on the species. Diplodium coccinum is summer-early autumn flowering so you need to push it into growth early to get it to flower. If you start watering at the end of summer/early autumn as you do with the other Australian terrestrials all you get is rosettes. If I want to get a good flowering from coccinum I usually start watering from the last week of December/start of January (June/July in Nth Hemisphere). On the other hand my Diplodium grandiflorums (which flower in late autumn/early winter) flower well if I water them in late February/early March (August/Sepember) with my other terrestrials.
For the robustum and truncatum you've just got from Nesbitts, robustum flowers around mid-autumn so I usually start watering this species within the last 2 weeks of January (July). truncatum is an early autumn flowering species so I usually water from the start of January (July). Diplodium truncatum is a shy flowering species though. It seems to flower better with a cool summer but even then you don’t get many flowers in the pot.
The challenge with watering early is trying to keep them cool enough during the summer so that the tubers won’t rot. That may not be a problem in NY though.