Power sequencing of simple peripheral ICs for ADC/GPIO with an MCU
It is common practice to connect both ICs to the same power rail and to reset the ICs some time after the power lines are "up". This reset is usually generated using a resistor and a capacitor, the charging of the capacitor takes some time and during that time the chips are kept in reset mode. Only after some time (when the power lines are OK) the reset will be released.

Probably the MCU's ADC will not even be connected to the input pin at startup, you might have to enable it in software first.

Separating the power rails actually increases the chance to have a situation where one IC feeds the other IC through the ESD protection diodes. That usually does not damage anything but it is an undesirable situation nonetheless. The VCC +0.3V or 6V, whatever is lower requirement of the MCU is there to prevent this situation. For an explanation on why and how, see the video Dave Jones from the EEVBLOG made here.