I doubt the relevant departments confiscate animals one day and hand them out the next. The process of finding them new homes takes some months. I am sure also that the relevant departments will make every effort that the animals they hand out are as healthy as possible.
There is process here and I am sure it will be strictly followed. Perhaps Jeff could explain the process for NSW?
That said one of the outbreaks of IBD in Victoria was traced back to a zoo which had temporarily housed natives with confiscated exotics with dissasterous results. The recipient of the infected animals lost their whole collection and I think they ended up burning their enclosures as a precaution.
You cannot be to careful. If you are getting animals from an unknown or suspect source ideally you will want to quarantine them for as long as possible. You also want to control other vectors such as mites and take precautions such as washing your hands or using one of those sanitising gels between handling anything to do with each animal in your collection.