I've set the replicator to only replicate a 'customers' table. However, on the assessment page, I see a connectivity problem saying the user doesn't have read permission on 'customers2' table.
Steps I took:
Create a database with a 'customers' table and 'customers2' table.
Create user1 with permission to read both tables.
Create user2 with permission to only read the 'customers2' table.
Create a replicator draft using user1 in the source. Select all tables to replicate.
Go to the assessment page
Navigate back to the source step and edit it to use user2 as the user.
Select only the 'customers' table (only visible one)
Continue to assessment, note a connectivity error for 'customers2' table.
I suspect you don't need to go through all these steps to reproduce, probably can do it with one user, and just editing the tables selected. Though in that case you won't see the connectivity issue.