When I say a spiritual Atemi, I simply mean, that he/she as the aggressor have by intiating an attack have created an "unnatural" situation. If you are also in the wrong, for whatever reason, it will be intrisically more difficult for you to conteract the disharmony. Your positive spiritual atemi is required. Should you respond with hate, the attacker now has a better reason to attack. If you maintain the spirtual calm that we all strive for, the attacker could theoretically be subdued by your lack of aggression.
A ki atemi is far more "physical." Everyone has a ki field, whether you belive in it or not. Developing ki, though no simple task, can be done by anyone with the proper relaxed mindstate. Hopefully, your ki is more developed than your attacker's, in which case techniques may not be necessary. Extend though the attacker, and strike them with your ki!
Atemi on the mat degrades the lesson. Don't muscle through techniques! Use ki for better results.