Minimal presentations are special cases of FI-Reps. But the RIVET formats for the two are incompatible. This means in particular, that if you compute a minimal presentation via the -- minpres flag, you can't open it in RIVET to visualize it or print its Hilbert Function/ Betti numbers. (The 0th and 1st Betti numbers are already there for you, but not 2nd.)
Clearly, the minimal presentation should be printed out in FI-Rep input format. As the one who wrote the print function for the minimal presentations, I don't know why I didn't realize this earlier.