I've killed 4 invaders in less than 10 seconds without them killing anyone else, I even did it with a hand canon and I didn't get the Not On My Watch medal , thus not completed the quest step.
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One possibility is that a team mate died for some other reason. I did it using the xenophage in 4-5 seconds. There was no Primevil heal notice, but when I turned around a fire team member had died to the primevil.