In patients using a tandem insulin pump on auto-mode/Control-IQ, would decreasing the basal settings on the profile actually reduce the delivered hourly insulin dose or is that only relevant if they switch to manual mode?  

In the control IQ, the basal adjustment IS relevant in Auto-mode. The algorithm uses predicted CGM reading in 30 minutes (in the future) and responds to keep the glucose by CGM in the targeted range. See below: Above 160 mg/dL, basal insulin rate increases Above 180 mg/dL, a correction bolus is...

The Tandem Control IQ differs from other pump brands in that the preset basal rate is still used even in closed loop mode; however, the pump will adjust the basal rate up or down if high or low glucose levels are predicted. In other models, the preset basal rate is not used at all in closed loop mod...