Technically, if you are not in uniform, you are supposed to put your hand over your heart, and presidents respected that until Reagan came along. He was big on Republican Theatrics and Propaganda, so he started doing the salute, and others have followed, although most mix it up.

Trump is the biggest hypocrite in American history, so he's big on the salute.

The president is the civilian who is in charge of the military. Definitely not technically in the military, by design. Other possible reasons to salute include wearing uniform or being a vet, which also don't apply.