...sometimes the banks are "nicer" to certain customers as well. From your story, they are not being nice to you and these are not "laws" you broke, just banking customs. If the contribution limit is $5000 yearly, then overcontributions should be based on yearly amounts as well, not monthly.
Is this the bank telling you this information, or the CRA? Don't believe the bank and don't hesitate to call the CRA.
I withdrew my TFSA for a deposit on my home and they tried to charge me over $100 to "close" the account. I told them to keep $0.01 cents in it or just keep it open at $0.00. They orginally told me I couldn't do either so I wrote them a letter, called a few times and withdrew all but $10 from the account.... they actually GAVE me $100 as an apology. I didnt' expect the gift, but...thank you!