Sorry for your losses. Remember ANY lifeform from ANY other tank can bring ich or velvet into your DT....No inverts do not "carry" ich and inverts lack the red blood that ich & velvet must have to survive and continue the life cycle - but it only takes ONE DROP of contaminated water from another tank to bring a nightmare into your tank - and when that drop of water brings the parasite to your tank - it's feeding&breeting time.
I imagine if you added the anemone within the last 2-3 weeks - that is your source of the breakout...Yes tangs are very susceptable to all skin parasites - but the parasite MUST BE IN YOUR TANK 1st....stress alone cannot "give" a fish ich. - while a "unstressed" tang will get ich just as fast as one that is stressed....
when you have a parasite that multilpies 256 times, everytime each one multiplies, you can have over a million of them in your tank within 10days, and before then, no fish left.
I suggest Qtine & teratment for your remaining fish immediately, but it sounds like your strating that process. Be prepared to treat the parasite with copper, hypo, or both. Also remember if the parasite is marine velvet - hypo does no good.