This immortality thing does create a plot-hole of sorts because back in Chapter 21: Return to Wave: Haku
Kiyomi said "If you make this change and become like me should you die that’s it." which implies that they are mortal. This could be a case of immortality = eternal youth, but they can still be killed by normal means.
Author's response
To me immortality and eternal youth are one and the same. They can still be killed via normal means but they aren't going to age.