Final exported video is very saturated and blowout even with the right export settings

I work for/with/teach pro colorists, some of whom were the team that DolbyVision hired to produce the in-house demo videos for pro colorists to master for Netflix et al. So I'm around all sorts of high-end color space gamut/volume/display discussions.

And still, HDR is definitely the Wild Wild West. Most pro colorists have yet to produce a single paid job in any form of HDR, though that will be changing over the next couple years I'm sure.

And for those that do, it's a total freaking mess! Right now, there are several possible forms, it's even worse than the VHS/Betamax days ... HDR10, HDR10+, HLG, PQ, DolbyVision, and variants thereof.

Next, most screens still do not support any form of HDR. And among those that do, they all have a limited selection of the above options, and don't do the others.

And further, a very tiny percentage of the screens that do support some form of HDR, do it adequately. "Correctly" ... well, not so much.

Grading on anything but a high-end reference montior is ... dicey. Flanders finally has a 65" monitor that is useful for pro grading, at a relatively CHEAP price of $19,000 USD. And their previous model was $29,.000.

All lesser cost monitors will be changing things on you, in the background, designed to protect the screen from burnout. So they will either lift shadows or drop highlights ... or both ... on a routine, fairly subtle basis, to protect the screen. Some monitors ... if you have the Service remotes for ... you can override some or much of that, though not all.

You do of course lose any warranty for that monitor on turning that option on.

Great, right? The screen shifts, it won't do it precisely the same, it's dang near impossible to 'see' what it's doing, so ... confidence in your grade is ... sadly ... about zilch. For professional needs.

For amateur stuff, have fun ... just don't expect to always get exactly what you thought you graded for.

So ... my questions after all this ...

1. in what player did you view that export?
2. and ... how does it look when re-imported into Premiere?
3.  what is your OS and monitor?
4.  was your OS set to HDR mode while working in Premiere?
5.  were the Premiere settings for Display Color management on, if on a Mac, the Extended Dynamic range option, and the display options for Premiere?

Tone mapping in Premiere Pro

Color management in Premiere Pro

Color space needs to be the same for clip, sequence and export.