Give them at least 48 hrs to adjust to tank conditions.
The "cheesing out" syndrome can be the result of limited nutrients (Phosphates, Nitrates). Zoanthids need fish poop, dissolved food matter and the resulting nutrients to thrive.
generally, zoanthids can thrive in the same conditions that SPS corals do. Good dissolved organics levels, high light, good nutrient export, low nutrient byproducts like Nitrates and Phosphates. I am not claiming that Zoanthids need the pristine conditions that SPS corals require but they do thrive in similar conditions. However, I have learned from experience that Phosphate levels below .02 can be detrimental to the health of the polyps. Always remember that Nitrogen and Phosphorus are the building blocks for coral life, so zero Nitrate reading or zero Phosphate reading are not a good thing for your aquarium life.
Zoanthids do not require the level of, or the amount of trace elements that SPS corals do but they certainly benefit from consistent water quality/chemistry. Qualities that should be monitored regularly in a reef aquarium are -- Alkalinity, Calcium, Magnesium, Iodine, temperature, Phosphates, Nitrates, and pH. I am not indicating that they require all of the aforementioned items specifically, only that consistent levels keep Zoanthids happy and healthy. My chemistry is consistently maintained in this range:
dKH: 8.0 - 9.0
Calcium: 430 - 440
Magnesium: 1250 - 1300
Iodine: Maintained via regular water changes (be careful if you are dosing without testing!)
Temperature: 77 - 79 degrees
pH: 8.1-8.2
Phosphates: .02 - .03
Nitrates < 5
Adding iodide weekly also benefits them