As Wells Fargo & Co.’s sales-tactics scandal unfolded, investors, regulators and politicians asked how improper practices could have persisted for so long. One possible reason: Bank branches were given a heads up before Wells Fargo’s internal monitors landed for inspections.

Managers and employees at the bank’s roughly 6,000 branches across the U.S. typically had at least 24 hours’ warning about annual reviews conducted by risk employees, current and former Wells Fargo employees and executives said. That gave many employees...