The correct procedure is to start at the valve stem while dismounting a tire and work both ways around to the opposite side. Start opposite the stem and work your way around to it when mounting a tire. Following this protocol will dramatically reduce the odds of a tube pinch or tear during tire dismounting/mounting.
You are 100% correct.
I change m/c tires on top of an automotive wheel/tire assembly on the shop floor. This gives me some elevation to put my knees on the cycle tire and protects the disc from bending. I encourage my customers to watch me change their tires.
Dismount from the valve stem to our knees (or body if working on an up-right stand). Remount from our knees (or our body) to the valve stem. Always keeping the engaged portion of the bead Down in the drop-center.
Remove the valve core, loosen the nut to the top of the threads, if bead locked loosen its nut to the top of its threads and dis-lodge the bead lock from the beads.
Break down the beads on both sides.
With disc facing down in the auto wheel, with my knees on top of m/c tire opposite of the valve (or one could insert a Bead Buddy to hold bead down), insert the hooked end of two tire irons into the beads about 2 inches apart, one on Each side of the valve stem.
Using a third iron (or even 4 irons), alternate removing only another 2-3 inches of bead at a time from LH side / RH side, moving the 2 hooked irons closer to the still engaged portion of the bead. Working towards my knees.
Installation with usually a single flat tipped iron (the iron should only be inserted about 1/4 - 3/8 inch past the edge of the rim) is performed from my knees, alternating sides back towards the valve stem. Moving my knees as I work towards the valve stem. Keeping the bead compressed into the drop-center of the rim. Push the valve stem with nut attached to only its tip into the tire as we install the final 2-3 inches of bead.