Bending the linings with the bending iron to fit the curves is much easier than bending the ribs. Once they're shaped, you can trim the linings until they're very snug in the mortises. You don't want to cut them too short.
Clothespins wrapped with rubber bands are cheap and very effective clamps to hold the linings in place. You can start by putting a pin-clamp any place their might be a little gap, then work your way out from that point.
Although hide glue dries well in about 4 hours, it's always safer to just let joints sit overnight before removing clamps.