$4,000 cash deposited into a bank account.

45 minutes a $3,500 cashiers check is purchased - same customer, new trip to the branch.

Monetary instrument log?
Fincen says you have to report on the log if the customer first deposits into his account and then buys. so I guess my question is the definition of "first" - does the 45 minute gap between transaction eliminate the need to place on the log.

According to the FFIEC manual, the Indirect Currency Purchases of Monetary Instruments does require recordkeeping when the cash is first deposited into the account and then the purchase is made using the funds from the account. (Revised manual dated 2014, page 101)

Without knowing all of the facts, I can imagine how this could happen.
Customer comes to bank to deposit cash.
Customer goes to purchase something, expecting to pay with a personal check. Seller says "I need a Cashier's check."
Customer comes to bank to purchase Cashier's Check.

IMO, the cash deposited was used to purchase the cashier's check - regardless of the time that passed between the two transactions.

It's OK - Using your scenario, I would have to disagree. Customer's intent in depositing the cash was not to purchase a negotiable instrument. I would not complete an MIL for the subsequent Cashier's Check purchase.

As indicated, examiner A would say "absolutely." Examiner B would say, "Naaah."

Just log it and go on to what's next.

I believe that the exam manual's comments were largely in response to banks that were avoiding maintaining monetary instrument logs by requiring cash to be deposited prior to the purchase. That being said, I would err on the side of caution and log the purchase since you have knowledge of it. The chances of being criticized for not logging it are greater than the chances of being criticized for logging it. One word of caution would be to make sure whichever decision you make, make sure you do this consistently.