AD7124-4B has two independent power supply pins: AVDD and IOVDD.
According to ABSOLUTE MAXIMUM RATINGS, there seems to be no order of the turning on/off the power.
Is it right?
The datasheet doesn't mention anything about it so there should be no issue about power sequence. It doesn't matter whether you power up AVDD or IOVDD first.
I don't know if it's needed, but if you look at the AD7124-4 eval board User Guide schematics, you will see they use the ADM1185 power sequencer to bring up IOVdd after AVdd.
This was used to prevent any conflict with the SDP board. However, the part does not have any special needs in terms of power supply sequencing. AVDD or IOVDD can be powered up first. The only thing to consider is that AVDD is present before any analog inputs (external reference for example) to the part are powered up. If the part and external reference use the same power supply rail, all is good. Similarly, IOVDD should be present before digital signals are applied.