It's not that he cares; Dabi tells himself making sure his teammates don't die is just the bare minimum. He ignores the feeling stirring up inside him.

When bandaging your unconscious body in bed, his selfish motives override most genuine concerns—or so he desperately claims. It's not that he cares.

“You better not die now...”

However, even while mildly annoyed, he still made sure that damn hero who damaged you became proper fuel for his flames—because how dare that filth hurt you?