mandarins usually keep close to the rock and substrate. There isnt anything about an anemone that looks like the normal terrain that a mandarin will swim around/in.
I had three anemones in my tank at one point (I have two now, had to sell the large one) and the mandarin never gets close. He just swims on the rock and substrate, and when he sees the anemone, he will move away from it.. and onto the next rock.
They may be slow, but they arent stupid. I dont think its likely they will swim into your anemone. Unless you scare them and they dart across the tank and into the anemone on accident. Either way, A bta probably wont mean its death.. a carpet anemone may be a different story.
If you are really worried, pick up a clown to host the nem. If the clown is in there defending its turf, the mandarin wont go close to it.
Jess