I think this is simply a problem of not understanding the new and frankly often confusing color management. And I work for/with/teach pro colorists btw.
First, although one can work in HDR, it is very much the Wild Wild West of video. Many screens can't do it at all yet, and those that supposedly can are all over the place in what they choose to do with the image. I don't really recommend working with that format at this time other than for learning processes.
So turning off the HLG/HDR setting of the iPhone is as a practical thing, I think wise. But you've already got HLG clips, so this is what you should do.
HLG Clips used in Rec.709/SDR Workflows
- Select one or more clips in the Project panel bin
- right-click Modify/Interpret Footage
- at the bottom, set the Override-To option to Rec.709
- with the Timeline panel active, set the Sequence Settings Working Color Space to Rec.709
- turn ON the Auto-tonemapping option
Doing the above will cause Pr to bring those clips properly into the sRGB color space of a Rec.709 workflow. And will remap the dynamic range to within Rec.709 limits without clipping whites or crushing blacks. It's a decent starting point for "prettifying" the image in the Color workspace Lumeter panel by yourself as the next step.
If you really want to, I can go into an HDR workflow setup also.
Plus ... for Mac users, there is now a setting which might get you a correct Rec.709 image with both the camera and the display transform applied, which the standard Rec.709 in ColorSync does not..
Check your system or monitor settings for the option for "HDTV/Rec.709/Bt709 Bt1886" and use that setting. Then turn off the gamma boost option in those settings somewhere.