This mod doesn't do anything with achievements, so I'm not sure why you're having this issue.
I can tell you however, as a modder I am constantly restarting the game and loading into new or existing worlds. Because the game keeps track of modded achievements separately from vanilla, mine get constantly fucked up, and I get new achievements all the time despite having them already, and I have no idea how to fix it.
I wish I could be of more use, sorry!