I don't claim to be an electronics expert, but here's how an EE explained the basics of VFD's to me:
The VFD takes in 60 hz power, single or three phase.
It then proceeds to convert it all to fairly high quality DC power on the "DC Buss."
The big transistors then use the DC power to generate the output 3 phase AC power at the frequency and voltage needed.
I think the 1 phase input and 3 phase output hook-up is considered an "off label" use by the manufactures, but this is a well known application.
Someone else may have to correct me on this part, but I believe that you have to de-rate the VFD when running 1P to 3P.
In other words, if you want 2 HP, 3P output, you might need a VFD rated for 5 HP when you only feed it 1P.
Terry S