Summary. Whenever you use a custom illuminant to make a printer profile, use M2 Measurements or OBA free paper.
I1Profiler can take measurements that are based on M0,M1, and M2 where M1 has full D50 uV levels and M0 has about 2/3rds of the uV that M1 has. When one of the M illuminants is selected to measure a chart, the measured data includes whatever the M1/M0 uV part bumped the visible blue part of the measured spectrum. For instance, 440nm is often bumped to 120% reflectance! This is then factored in as if the paper reflected these levels of light from the custom illuminant. Whether the custom illuminant has a lot or little uV is ignored. For that matter, custom illuminant spectra only goes to 380nm. While some of this would be converted to visible light I1profiler has no way to know and simply treats it as regular visible light (with little effect at these wavelengths).
Since most custom illuminants have relatively small amounts of uV, measurements made with M0 or M1 should not be used on any paper with significant OBAs as they will significantly distort the profile.
Another reason to avoid OBA paper.
Added:
This is an example of how M1 measurements distorts I1Profiler profiles. I used a custom LED illuminant with no uV (very little light below 420nm and less than .01 below 410nm). The LED doesn't activate OBAs. Using high OBA paper and this LED custom illuminant there should be no difference between M1 and M2 profiles. But making a profile using the M1 measurements I get a white point that has a b* of -14, a pretty blush white and it soft proofs with a strong bluish tint using show paper color. With M2 (uV cut) and the same LED illuminant, the white point is near neutral and the soft proof is no longer shifted to the blue.