I planted Irish Moss a month or so ago and it is doing great. I think they are the same. Mine gets full sun and we have also been experiencing terrible heat and humidity. But maybe you have over watered it? I think that is what I did to some newly planted candytuft because it is turning yellow and we have also had a lot of rain this spring and summer. Try to cut back on watering.

From what I have read, Moss likes Acidic soil. When I planted mine this year I sprinkled the area with Aluminum Sulfate 0-0-0, and then sprinkled some compost on top of that. I wet the area and then pressed down my moss and watered it again. It seems to be doing well, except for a couple pieces that some critters dug up. I must have been covering their "stash." I also use a 10 foot mister every few days when it is dry outside. The website listed below is a pretty good resource about moss. But their misters are expensive. I got one from LandscapeUSA.com. It's apparently supposed to hang under Patio umbrellas to keep cool. But I use mine for my moss/fern area.

Here is a link that might be useful: Moss Acres

Mine are in the shade and I found the earlier in the spring I established them, the better they did. My husband planted some in a very sunny, dry zone and it died almost right away, despite watering it. I can't believe these things will thrive in full sun despite what the directions for planting say. It's a lot of work to keep it wet enough with the heat.