I have a Tek DMM4020, which is literally a rebadged Fluke 8808A. It's an absolutely fantastic meter and is my bench workhorse.
The behavior you're describing is absolutely not correct. When you power it up, it should default to DCV Auto. In that mode it should auto-range 100% of the time without you having to do anything. (The only exception to this I've ever encountered is when I tried to measure 1000V when it was in auto mode. It caused the meter to lock up, which is the only time I've ever seen that happen.)
If I were you I'd return the unit. It sounds like there's an issue with the main MCU (an off the shelf MSP430) or the ADC.
If you do go this route, keep an eye out for the Tektronix 4020 when looking for a replacement. These sometimes go cheaper than the 8808A because people don't realize it's the same meter