Yes, you understand it porperly.
There are four phases of closing for each park.
Phase 1:
. . . The toll booths are closed to everything except Disney buses and CMs on duty.
Phase 2:
. . . All ticket sales stops.
. . . Unless you already have a ticket in hand you are not allowed in.
Phase 3:
. . . Only Resort Guests and Annual Passholders are allowed in.
. . . If staing at a Disney Resort without tickets on the room key you may be asked for ID. . . . If the tickets ae encoded on your room key, or you have an AP the biometrics must match.
Phase 4:
. . . The parks are closed to everyone.
NOTE:
If you show up at a park and you would normally not be allowed in due to a phased closing, and you have dining reservations in that park, it does NOT make any difference, they still will not let you in.