Is it possible for LTM4622 to generate negative output? Just like the one described in LTM8025 or LTM8065 datasheets (attached)?
Sorry for any confusion, I should have clarified that if using both outputs in neg. configuration that would normally be for the case that the output rails are being paralleled (ie for higher current capability).
In the case of using both rails otherwise for this, the part cannot provide two different negative output voltages since the GND pins for channel 1 and channel 2 are internally tied. If one would try to generate two different negative outputs (ie ground Vout1 & Vout2) they would find the outputs would fight to try to regulate to their programmed output voltage.
In your case where you only ground one of the outputs (ie Vout1) then you are correct Vout1 will regulate the correct output voltage, and Vout2 would regulate at programmed Vout1 + programmed Vout2. As you noted Vout2 voltage with respect to system ground is dependent on Vout1 voltage, so excursions on Vout1 voltage (ie load transient, start-up) will also show up on Vout2.