If you look at the origin of this phrase it becomes clear that is a concept formulated by psychologists:
Passive–aggressive behavior is characterized by indirect resistance to the demands of others and an avoidance of direct confrontation.
Originally a scientific term that was well defined,
Passive–aggressive behavior was first defined clinically by Colonel William Menninger during World War II in the context of men's reaction to military compliance. Menninger described soldiers who were not openly defiant but expressed their aggressiveness "by passive measures, such as pouting, stubbornness, procrastination, inefficiency, and passive obstructionism" due to what Menninger saw as an "immaturity" and a reaction to "routine military stress".
It slipped from technical terminology to everyday (kitchen) psychology jargon. Both of these are a source for the source of this usage in German. It is not even an English loan word. It is a Latin construct in both language and used in both languages in exactly the same manner with the same meanings.
It is a perfectly well established concept and phrase in German:
Karrierebibel: Passiv-aggressiv: Definition, Anzeichen, Tipps
So the associated patterns to observe for this description are:
non-active resistance to expected work requirements, opposition, sullenness, stubbornness, and negative attitudes in response to requirements for normal performance levels expected by others, indirect behaviors as procrastination, forgetfulness, and purposeful inefficiency, especially in reaction to demands by authority figures, passive, sometimes obstructionist resistance to complying with expectations in interpersonal or occupational situations, avoiding direct or clear communication, evading problems, fear of intimacy or competition, making excuses, blaming others, obstructionism, "playing the victim", feigning compliance with requests, sarcasm, backhanded compliments, and hiding anger, deliberate, active, but carefully veiled hostile acts which are distinctively different in character from the non-assertive style of passive resistance, "The worst case of passive–aggressive behavior involves destructive attitudes such as negativity, sullenness, resentment, procrastination, 'forgetting' to do something, chronic lateness, and intentional inefficiency."
As is evident from this laundry list the accompanying personality disorder is not considered very useful anymore and no longer part of the DSM V. Some of the associated pattern are falling just short from being simply openly aggressive, some of them are perfectly normal behaviour for a healthy individual that is forced into an authoritarian environment or situation.
The overuse of this phrase in ill-fitting contexts by people using it as a kitchen therapist has led
to the funny situation the those who utter the term are often engaging in passive-aggressive behaviour just by that. In most interpersonal encounters the term the should have been used or what was really meant is something like feindselig-negativ. But "avoiding direct confrontation…"
If an English native speaker wants to say "passive-aggressive" in German, he should say passiv-aggressiv. If the same speaker wants to say something that is a little bit more concise, to the point, less jargony he should do so. Some examples or suggestions are found below the question above.