Please clarify my understanding for processing a verbal notice of a Reg. E claim on a signature-based VISA debit card transaction.

Our processor for VISA will not start an investigation until a customer’s written notice is received from us (We do require written notice after receiving a verbal notice). Under Regulation E we have to begin our investigation from our customer’s verbal notice. If we determine that an error did occur within 10 days, we would credit back the customer the amount of the unauthorized transaction (less the liability amount) satisfying our Reg. E obligations. When we receive the customer’s written notice, we would forward it on to VISA for their investigation. If customer is provided zero liability we would credit back the customer (less the liability amount).

You are correct in that Reg. E doesn't allow you to require a written notice and that you must begin your investigation when you get the oral notice. Your clock starts at that time for Reg. E anyway.

I don't know that Visa allows your clock to start only AFTER you get a written notice. If it does, you're following those rules. If it doesn't, you need to follow the zero liability rules and the 5 day provisional credit rules Visa imposes and which you contracted for.

If you apply the Reg. E liability and then, properly following the Visa rules, determine that zero liability was applicable, a recrediting would be required. If the Visa rules do not allow you to require a written notice (forget about vendor requirements with your investigation vendor, focus on your agreement with Visa and with your customer) then you need to follow all the rules from the time of the notice, i.e. zero liability and 5-day provisional, when it is through their network.