The stage where the parasite is attached to a fish is called a trophont. The trophont will spend three to seven days (depending on temperature) feeding on the fish and that is what you see symptomatically when you see "salt sprinkled on the fish" even though this is actually under the skin not on top of it.
After that, the trophont leaves the fish and becomes what is called a protomont. This protomont travels to the substrate and begins to crawl around for usually two to eight hours, but it could go for as long as eighteen hours after it leaves it's fish host. Once the protomont attaches to a surface, it begins to encyst and is now called a tomont.
Protomonts will not attach to inverts. However, in display tanks, substrate is the attachment of choice. The remainder of the life cycle is why you should leave the display tank fallow for 9 weeks (some say 10 weeks) If you do not transfer water after quarantining corals or other inverts, you will be quite safe.
Division inside the cyst into hundreds of daughter parasites, called tomites, begins shortly thereafter. This noninfectious stage can last anywhere from three to twenty-eight days. During this extended period, the parasite cyst is lying in wait for a host. After this period, the tomites hatch and begin swimming around, looking for a fish host. At this point, they are called theronts, and they must find a host within twenty-four hours or die.
In theory it is remotely possible to have a theront brought in with a coral although it is highly unlikely. But that is what the three day isolation (and in my case dip with Revive or Coral Rx) is for.