I need help with Due To and Due From accounts

I am new to the idea of a due to and due from account system with our books so I am having some trouble clearing up my confusion. I greatly appreciate any help.

I work for a company and we have two quickbooks desktop files for our two bank accounts. The first one is for our Operating account, the second one is for the Activities account. Utilities and operating costs are cut out of the Operating account and fundraisers for trips and sports events are paid out of the Activities account. 

Sometimes due to an emergency situation or amount of funds available, there will be costs that need to be cut out of the Activities account that get cut out of the Operating account. Our accountant has set up a Due To/From system in both of the company files.

I have ran the report in both company files to get the total that is Due To the Activities account and the amount that is Due From the Activities account and vice versa for the Operating account. My confusion comes with the reconciliation, am I supposed to have a matching total on the Due To Activities and the Due From Activities? Will I be entering the transactions in both the Operating and the Activities account to get the totals to match?