The color management in Safari and some other Mac applications will only apply color correction for the primary display (the display with the menu bar). When a window is moved to the secondary display, the correct color correction for that display is not applied. This causes the images to be over-saturated on the secondary display. To display colors correctly on the wide color gamut display it must be made the primary display. Use the Mac OS System Preferences - Displays to configure the display as the primary.
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