Why do the accounts' register show the $amounts from the prior closed fiscal year?

Hello referrals, 

The account registers will always show all the transactions associated to it. This is regardless of the status (reconciled, clear, and blank) and when you closed the books.

Closing of books only affects the data that shows on your reports. If you set password when you closed the books, QuickBooks will prompt you to enter it if you create a transaction dated prior to the closing date. You can use this link to know more about the closing of books: Close your books to lock past transactions.

Also, you can consult your accountant for further explanation about this. They know exactly what are the do's and don'ts after you close your books.

We'll be right here if you require additional assistance regarding your register. Have a great day!