Colour difference in export while settings are all similar.

You're on a Mac, right? Without reference modes also, I'd wager. I'll give some information on the why, and then what the options are down below.

As if you are on a Mac without reference modes, thanks to Apple, you are where you are. Because in all their wisdom, Apple chose to use a "unique" display transform function for Rec.709 video. Rather than following the long-published standard, which requires a display transform function roughly equivalent to gamma 2.4, Apple uses roughly gamma 1.96.

And worse, according to some high-end sleuthing by a colorist I'm aware of, their color space transform from Rec.709's sRGB to the native P3 space of the monitor is also a bit wonky. So not only is the image off in tonality (looking brighter than it should) it is a bit off in color, not just slightly desatuarated, but the hues are also off a bit.

I would add that "upper end" Macs, with Reference modes for their monitors, have the HDTV setting ... which does apply correct display transforms for both tonality and color. So it's only Macs without reference modes that suffer.

So what to do?

First, realize that your viewing outside of Premiere whether in QuickTime Player, Chrome, or Safari, is not what any PC user, any broadcast compliant system, or most Android and TV devices will see.

Second, then make a choice as to what is important to you. You have a couple different options in Premiere's greatly expanded color management settings. Found in the Lumetri panel, the Settings tab. The one named Settings.

To begin with, most users should have Display Color Management set to On, unless you are running a fully calibrated and profiled monitoring system set for a tight Rec.709 performance. If you don't know what separates a calibration and a profile, you ain't. Stick with DCM on.

For most Mac users ... if all you are really concerned about is how it looks on your rig, and mainly other non-reference mode Macs, then set the Viewer Gamma to 1.96/QuickTime. That will tell Premiere to use the Apple style odd display transform. The image will look similar then in QuickTime player, but way too dark in VLC, and on most non-Mac screens.

Or, if you want to stick to The Standard, so the output is in the 'middle' of all devices, the question is what is your viewing ambient light environment when doing your color work? 

It is your viewing environment lighting when grading that determines how the monitor display gamma should be set while grading.

If you are in a moderately light to fairly bright 'office' type lighting, set the viewer gamma to 2.2/Web. NOT becasue "the web is gamma 2.2" ... as that only applies to STILL images. Rec.709 media on the web is still assumed having been graded on a gamma 2.4 screen in a semi-darkened room that is pretty darn dark. 

IF you are not in a semi-darkened room, the Rec.709 specs call for setting the monitor display transform to gamma 2.2. Which actually should  be used by a lot of people as they don't have that darkened room.

If you are in that "properly" semi-darkened room, a pretty dark space though not "black", and with neutral wall or surface behind the monitor, with a proper bias light on that surface, then use the gamma 2.4 setting.

As someone tied into the pro colorist community, with a reference monitor calibrated and profiled, knowing what those profile charts show, and in a carefully nuetral gray surround on all wall surfaces, with D65 bias lights at a measured amount on the curtain around the monitor ... I run grading using gamma 2.4.

Because I am in that semi-darkened room. With a monitor carefully set to match the standards.

Finally, remember ... no one else will ever see exactly what you see on your screen.

Colorists are taught that right off. You don't grade in a darkened room and set the  monitor to X so anyone sees what you see. They won't. You do so, so that your outputs, on all other screens out there, look like other pro-produced media on that screen, no matter what it is.