The Ligue 1 champions progressed to the quarter-finals after a 2-2 second-leg draw at Stamford Bridge, when Zlatan Ibrahimovic was controversially sent off after just 31 minutes.
The Swede was dismissed for a challenge on Oscar and will now miss PSG's last-eight first leg.
Full-back Aurier, who sat out the last 16 second leg due to a hamstring injury, was critical of Kuipers' performance in a video posted on his Twitter account and will now face UEFA scrutiny.
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