Yes, you are correct. After the calamity ends, the records are restored (even photographs), and some (maybe all, maybe none) of the memories.
Tatsuji keeps careful records of all classes 3-3. Since he reveals the truth about Mami in 1998, the data was already restored.
It is not shown, but he probably also tracks the deaths.
It is not shown if Tatsuji's memories were erased or not. We know that the records both written and graphical (photographs) are edited and the extra removed - and later repositioned - name and image. But the memory of the calamity is not erased. People know that deaths occured. For someone tracking the calamity for as long as Tetsuji, and that know of the phenomena around the extra's records could spot a blank where something should be there. The calamity does not prevent discovery of the extra through sleuthing.
He could restore the information by crossing data from the records. The "extra" would be evident because there is no enrollment papers, no admission exam score, etc. Also the duplicate name.
As people remembering, it is blurry. People involved in a calamity class usually die or won't want to remember or keep themselves involved with the school.
So probably when Mami returned (or anyone else, for that matter) nobody that once knew her in life was there to remember.