Not colored, but filtered. At least for the specific "orange" image. The other images are since they're different types of sensors.
If you view the sun with eclipse glasses, you basically see the "orange" image just with your eyes. Add the same level of filtering to a telescope or long lens on your camera, and you can capture similar image.
As you mention, the leftmost image (the red "photogram" intending to show intensity) is filtered. I'm writing mostly to amplify your comment because I spent some years working with these images.
People may not be aware how strongly filtered it is. The PHI imager is using 6 very narrow (<<0.1 nm) passbands, all centered about one absorption line (Fe I, 317nm, as you mention). It's insanely narrowband.
From the abstract of the paper (https://arxiv.org/pdf/1903.11061) describing the instrument:
> SO/PHI measures the Zeeman effect and the Doppler shift in the Fe i 617.3 nm spectral line. To this end, the instrument carries out narrow-band imaging spectro-polarimetry using a tunable LiNbO3 Fabry-Perot etalon, while the polarisation modulation is done with liquid crystal variable retarders (LCVRs). The line and the nearby continuum are sampled at six wavelength points and the data are recorded by a 2k × 2k CMOS detector. [...] The high heat load generated through proximity to the Sun is greatly reduced by the multilayer-coated entrance windows to the two telescopes that allow less than 4% of the total sunlight to enter the instrument, most of it in a narrow wavelength band around the chosen spectral line.
(Note: the 4% figure is just the pre-filtering at the entrance window, before the even sharper filtering done by the etalon.)
So the image you see is just a reconstruction of intensity using the 6 extremely narrow filters (I'm not sure precisely how they do the reconstruction; an analogous NASA instrument called HMI uses the straight average IIRC).
So, the remarks nearby about the black body emission of the Sun, etc., are correct but not relevant to the color used. The red color is just as easily viewed as the traditional coloring used for the scalar intensity represented by this image type, kind of mnemonically related to the fact that the FeI line at 617nm is in the red wavelengths.
In writing journal papers using these images, sometimes people use the longer but techically correct "pseudo-continuum intensity image" rather than the punchier "photogram". This emphasizes that the image shown is a reconstruction of the continuum intensity.
And as you say, the other "images", including magnetic field and velocity, are reconstructed using other algorithms from these 6 wavelengths. For instance, velocity is recovered because the Fe-I absorption line's location shifts with Doppler velocity along line-of-sight.
And magnetic field is recovered due to the Zeeman effect on the line shape.
It's amazing what you can do when you have so many photons!