This mod is built using an older, buggy version of the game.
If you want to play the bugfixed version, you'll need to download and play the main branch, as the mod author hasn't yet posted an updated version.
Make sure to double-check which version you're playing.
OldPapaSoul has created an updated version that has a lot of bugfixes, but hasn't had an opportunity to upload it to Itch.io yet, so it's only available via a link in the devlog.
... Actually, I believe that this exact bug is specifically addressed in that update.
You're likely playing on the older version of the game.
The developer has created a new version that has a lot of bugfixes (including this exact glitch), but can't update the version on Itch.io because of Game Jam rules.
To play the updated version, access the devlog (which can be found just under the download links) and download the new version from the link found there.