Currently, our safe deposit box charge assessed by an autocharge to an inactive account will cause the account to change status to active. I do not believe this charge although authorized to be auto charged originally by the customer should be regarded as a customer initiated transaction to the inactive account. Any thoughts on this?

I would agree that it should not be regarded as a customer-initiated transaction.

We require a customer signed debit to activate our dormant accounts.

And I think the definition of "activated" for escheat purposes is governed by your state escheat laws. Auto charges don't meet this definition because these can go on for years with no customer intervention/knowledge. At least in our state.