Dates entered within custom date fields for Account and Contact Modules are not automatically copying?

Dates entered within custom date fields for Account and Contact Modules are not automatically copying?

I have customized two date fields within the Account and Contact Modules. The fields are duplicate with same names. 

I entered the dates within the custom fields when I added a new record within the Account Module; then I added the new contact for that record within the Contacts Module thinking that the dates would have automatically duplicated same date info in the Contacts Module. Instead I had to duplicate my efforts manually. Shouldn't the dates I entered within the custom date fields duplicate automatically as long as I am within the same record and were named the same? 

Thanks for the help..