|In the past, phone cameras operated using the sRGB color space. Internet sites used sRGB. No mismatch, no problem. Some new phone cameras use a bigger color space. Apple iPhone 7 uses DCI color space (Digital Color Imaging) which records and displays a bigger range of colors. Good article HERE.
I believe DPC uses internet standard sRGB. If I try to upload an Adobe RGG color space image, the colors I see on DPC typically don't match what I see on my color-calibrated monitor. If I convert to sRGB first and set my software to view in sRGB, then the DPC version looks closer to what I see on my computer. An older DPC tutorial suggests converting to sRGB when preparing images for submission (HERE).
I presume uploading directly from the phone to DPC will result in conversion to sRGB by the DPC site (unless the phone export already does that). Presumably the image will have somewhat different colors than what you saw on your phone.
If the original DCI color space image arrives at Photoshop, using the first choice you show instructs Photoshop to abide by the colors of DCI. That is the best choice for preserving information, which should result in fewer artifacts during processing. How it looks on your monitor will be affected by how well you have color-calibrated your monitor, the gamut your monitor is able to display, and whether you have set Photoshop to display using "proof" colors or not. After any sharpening allowable under Minimal rules, you then would want to convert to sRGB and make the size correct for DPC submission. Otherwise I suspect the DPC upload process will make a conversion for you, with colors not ending up the same as what you see on your Photoshop screen.
Similar issue happens when I shoot Adobe RGB jpg images with my Nikon D800. Conversion to sRGB still needs to happen somewhere along the way to DPC (and can make a big difference in colors).
The challenge editing rules don't specifically address the matter of color space conversions, so perhaps someone who knows more than I do might want to join the discussion.