iPhone Footage Color not the same after export as in project

There is one other thing you're running into. You're on a Mac, right? Apple's created a massive headache by using an incorrect display transform for Rec.709 /SDR video files. That is I think what's your problem.

Bring the exported file back into Premiere ... does it look the same as on the sequence? As I expect it will ... if so, yea, it's Apple's fault.

And for that there isn't any good complete fix. Why?

The long-time standard display transform specified for Rec.709/SDR video has been gamma 2.4. However, Apple chose to use the camera transform figure, roughly gamma 1.96, as the display transform.

You simply cannot display the same file at two different display transforms and get the same look to the file.

You can also play the file in VLC or Potplayer, on your Mac, and it will probably look very like it did in Premiere. But not like it looks in QuickTime player, or Chrome or Safari browsers, because the later let Apple's ColorSync utility set the display transform.

VLC, Potplayer, and Firefox nearly always use the correct gamma 2.4 transform.

To make matters even more ... fascinating ... Apple has 'Reference modes' on some of their computers. Setting the Reference mode to "HDTV" gets the correct transform.

So what you see is not just different on a Mac, it's only different on some Macs.

In Premiere's color management options there's now the Viewing Gamma setting and you can pick what thou wist. 

You could use gamma 1.96/Quicktime and your file after you do your corrections, will look very similar outside of Premiere on your Mac ... as long as you are viewing without Reference modes, and in QuickTime Player, Chrome, or Safari.

Outside of your computer, most PCs, TVs, Android devices, and any Mac with Reference Modes wills see a much darker image.

Or use gamma 2.2/web, which is for when setting color corrections in a fairly bright working environment actually. 

Or use gamma 2.4/broadcast if you are working in a pretty darkened room, as a pro colorist would be doing.

The latter will result in files that will look relatively like unto normal pro produced media on most screens. As all pro Rec.709 is graded in darkened rooms using display transform of gamma 2.4.

But if you are not in a darkened room, do not use gamma 2.4 while doing your color worrk. Use gamma 2.2. Or 1.96 if you want to.