Ancient issue, by now. But sadly still here.
I assume you are checking Premiere's exports by viewing them outside of Premiere on a Mac without Reference modes set to HDTV, and in an amateur viewer like QuickTime player?
Because for some reason, Apple chose to set their ColorSync utility to use a wrong display transform for Rec.709 media. Seriously ... and as someone who works for/with/teaches pro colorists, many of whom are total Mac geeks, this has been infuriating for the last seven years or so.
Their color manglement utility (not a miss-spelling, intentional rephrasing there) ... uses essentially gamma 1.96, rather than the required gamma 2.4, as given in the specs for Rec.709/Bt.1886 video display transforms.
And you caught another issue ... not only do they use the wrong display gamma, they also didn't properly remap Rec.709's sRGB color primaries within the monitor's native P3 color space. Their chose display for Rec.709 video is off on both counts.
Hence any app that allows Apple's ColorSync to manage color, actually mangles Rec.709 video. Which include QuickTime Player, and the Chrome and Safari browsers.
Instead, use the VLC or Potplayer video players, which do not allow ColorSync to control display tranforms and use the correct transform/hue-remapping to the monitor. And Firefox browser.
This is only an issue on Macs that do not have Reference modes, set to HDTV. As Macs with Reference modes set to HDTV will use the correct display transform.
As will all other screens and devices.
Your PC uses the correct display transform ... as will most Android devices, all broadcast systems, and nearly all TVs.
No professional broadcast media is graded with the expectation of the (essentially) gamma 1.96 used by Apple's ColorSync utility. Period.
You can use the Viewer Gamma option in Premiere to set Premiere's internals to gamma 1.96 for the Program and Source monitors. Then when you color correct under that, you will get a simllar view in QuickTime player on that Mac.
But all viewers on correctly setup systems, including all broadcast compliant systems, and the vast majority of PCs, Android, and TVs, will see a very dark and over-saturated image.
Yea, it's a mess. But again, no professional broadcast/streaming is prepped at gamma 1.96. It's all done under gamma 2.4. You didn't notice this on that Mac though, I'll bet. What your screen is, is what you expect is correct, for most people.