Well it shouldn't be called the 'day it's due' then should it.
It should be the 'day it is over due'...
What kind of loopy logic makes sense of that.
Make dates and amounts clear otherwise you have no right to scare-tactic your tenants.
Behaviour like this should be investigated, if a landlord is overtly aggressive or difficult on rent, then they may have something to hide. Check your lease and compare it to state law.