As these plants are seasonal growers, it will not be much of a surprise that any such plant arriving from Australia will have to be adapted to the northern hemisphere. Although there are differences from species to species this general description should be applicable to most species. It may not reall surprise you: There are some species which adapt faster and easier whereas others will need more time to do so.

Tubers are available in Australia from about december to february, so they will arrive here in winter. Many may come already with new stolons in development. I usually plant them shortly after arrival using the substrate with some residual moisture. My way of producing such a substrate mix is by mixing moist peat with dry silica sand. I know that even this is not very exact and difficult to reproduce without further information. Let me describe the "moist peat" a little more: I use it when it clearly is moist (darker than dry peat) but so wet that the fibers will stick to your hands when grabbing it.
Alternatively, they can be planted once a stolon is in development. As this may be delayed by the dry conditions in the ziplock bag, I prefer to plant the tubers quickly.

The plants will most likely appear in spring and I usually try not to expose them to full heat and sunshine during their development in early summer as I prefer to give them a growth period as long as possible.
The first dormancy period will last a bit longer than for the already adapted species but usually the plants will emerge 2-3 months earlier than in the previous growing season. Please be aware that the plants are likely to be smaller than in their previous season and that trend might continue into the next growing season as well.
Despite having started late, the plants usually go dormant about the same time the adapted plants do resulting once again in a relatively short growing season. At least, the plants now mostly have found the new growth cycle.

As already mentioned the plants will loose size and strength during the adaption process and it will take several more years until they reach full size again. Generally it will take about five growing seasons for the adaption to complete and the plants to re-gain their strength, give or take a season for some species. For comparison, that is about the same period of time many species will need to grow from seeds to flowering size.

Especially tubers in the early steps of the adaption process may not produce a plant during the growing season but directly form a new, usually smaller tuber. Those are often the very difficult situations as now it becomes tricky to keep the right level of moisture in the substrate to avoid both desiccation and rot. The best way to handle such cases needs to be assessed on a case by case basis depending the tendency of that species towards rotting or desiccation. Not surprisingly, if and once a new plant grows from such a tuber, it once more will have lost some strength and size.