Whatever you do.., do not dip your anemone in the fresh water as it will kill it....I know one guy who did it...ugh. Anemones are mostly water as we well know.
IME of 34 years having anemones you do NOT need to quarantine them in terms of deseases or parasites. In fact, if your quarantine tank has marginal lighting and amrginal filtration your anemone most likely will perish in a few days. Don't forget, this creatures go through hell during collection and shipping...various salinity in the holding tanks, constant movement, natural settings will not be the same in a QT/Hospital tank either...and what if you had QT'd using copper or even less harsh methods of cleansing for fishes at some point...does one really want to attempt QT of inverts...shrimp, anemones and many more?
Just my 2 cents.