That was the case for people tasked to Aktion T4 and the like, and the various einsatzkommando, but not, for example, to members of the Wehrmacht who "swept up" after the SS in Ukraine, the Baltic states etc. Members of the Wehrmacht, being bound by the despicable oath of personal loyalty to Hitler, rather than to the Reich, were liable to summary drumhead court martial (often followed either by execution, or a commuted sentence to a penal battalion) for transgressing their oath/disobeying orders.
So it's a bit more nuanced than killing people because you swore an oath. It's also about the fact that if you were military and transgressed your oath to Adolf, your family would suffer too, from having your heritage investigated, to having your children put under special measures at school, or expelled, to being sent to Coventry. If you were executed, your family could expect "interviews" by the GeStaPo and possibly shipping to a concentration camp.