Those fittings look just like "flair it" fittings, and prolly operate in the same manner, which is pushing the pex over the barb, then sliding the nut to the fitting and threading it onto the fitting, that then crimps the line where it was made larger from stretching it over the barb.
Not many know it, but you can use the 1/2" white drinking water hose in place of 1/2" pex on "flair it" fittings, just in the case 12" pcs mite be used to quiet the pump.
The beauty of "flair it" fittings, is that
every RV supply and hardware store in the country handles them
They need hand tighten only
They cannot leak
and they are reasonably priced.,