Not sure about Mississippi, but a common method in other states and for postal votes is 2 envelopes. The outer one includes the voter's full info to be verified. The inner envelope contains their ballot. The outer envelope must be fully verified or rejected, then the inner envelope is sent to either the pile of votes to be counted, or the pile to be destroyed unopened.

Yes, a bad actor could skip process and identify how a person votes, but it would be obvious to everyone else in the room (and there are many people in the room watching for exactly this type of behavior).