The Magma site is extensive; I would toggle each header because stuff is located everywhere.Star Sizer
They are old school in that they will require you to call them and you get to talk to an actual well spoken young lady to place orders or inquiries. I would have Dan help you on the throat diameter and get what size he recommends with your chosen bullet mold and alloy and a cupped punch for gas checks.
She will know what you are asking for when you say "I need a .22X Star sizer die and a cupped .22 gas check punch for it". Their turnaround right now or at least this fall was about a week and the dies are 70 bucks, the punches I think are 25.
Check out the site for how to video instructions, which I'm sure you have.
The easy button for a production mold and production guns is .225 diameter and linotype or heat treated metal. IIRC, Dan is a lino/hardball alloy guy. Lino casts larger and might fit the throat better and with your mold might allow a larger size die, but its expensive and getting harder to find.
The instructions for the punch and die settings are here for lube hole spacing:Punch and Die Settings
She will ask for that too.
The Star sizer operates by having the bullet fed nose first. The gas check is applied to the base and the punch pushes the bullet through the die and the gas check is swaged through the die last, being indexed off of the bullet, rather than the opposite in an in and out sizer. The lube is pressurized with a handle and lubes the bullet when the punch is fully lowered (look at the hole spacing diagram). Another checked bullet is fed and as it is fed the finished bullet ejects from the bottom.