With Publisher 2.0.3 for macOS:
Create a new facing pages document with 1 page
Draw a small text frame on both sides of the master and link them together - ensure Text Frame > Hide Overflow is on for these frames
Go to page 1 and type into the frame - type more text than will fit and Publisher will show the overflow even though Hide Overflow is checked.
Toggle Hide Overflow off and back on to fix the problem
The problem will not occur if you just draw a frame on the right master, or if you draw the left frame but don't link it to the right frame. I've attached a document with two tiny linked frames for testing but this isn't document specific.
Overset Test.afpub