Earlier quoted context omitted.
That flies in the face of what I understand is true about diplomatic immunity. Citation required. As a less extreme example, diplomats can and DO park their vehicles illegally: in No Parking zones, Handicap Only zones, and blocking fire hydrants. Diplomat plates render the police unable to ticket them. It's civil not criminal courts, but for the exact reason that they are immune to our laws.
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Also, multiple countries have laws claiming universal jurisdiction. As I understand it, French laws against genocide denial claim to apply universally.
From your own discussion, it seems like "subject to the jurisdiction" should be understood as "can be judged in court". Diplomat is immune = can't be judged = not subject to jurisdiction. Immunity lifted = can be judged = subject to jurisdiction.