The ATmega328p datasheet says
The ADC is optimized for analog signals with an output impedance of approximately 10 kOhms or less. If such a source is used, the sampling time will be negligible. If a source with higher impedance is used, the sampling time will depend on how long time the source needs to charge the S/H capacitor, with can vary widely. The user is recommended to only use low impedance sources with slowly varying signals, since this minimizes the required charge transfer to the S/H capacitor.
The OP is using a 1.2M:100k divider. I'm guessing this has an impedance greater than 10kOhms. Switching between analog inputs will require extra time for the sample/hold capacitor to charge. Reading from the same input a second time allows for more settling time and is helpful with higher impedance inputs.