Hi David,
1) Physio Assistant: for most Therapy Assistant jobs, there is no qualification required as such. A lot of workplaces appreciate a First Aid certificate but that's it. There are some Physio Clinics/ Education providers that offer Physio Assistant Training modules. I would definitely recommend them, but they are not compulsory. Anyway, as a Physio you most likely wouldn't need it (they might just help you to familiarise with the NZ health system).
2) Work permit: There are different ways to acquire a work permit in NZ. Check the Immigration NZ website. Heaps of really good information there. However, work visa and essential skills work visa require a professional qualification that is recognised in NZ. Therefore, these will require registration with the PTBNZ. It is very unlikely that you can get a visa based on a Physio Assistant job, as this is not 'skilled employment'.
Try to apply for registration as soon as possible, as it might take a while to compile all the information (?and translations) and to complete the whole process. You also need to do an English test.
Good luck,
Fyzzio