The supply risetime seems unrealistic unless you are
applying an estabished supply through a load switch.
A DC-DC will have risetimes in mS or longer. Starting
from zero, everything in the reference is "playing
catch-up", large signal, not a small-signal stability
problem.
First step: determine whether the overshoot and
undershoot have any actual consequences. Who in
the bigger picture is ready to do anything with the
reference, 20uS after start of supply ramp? Bueller?
Second step, add enough output filter or overcompensate
the reference feedback loop to make reference rise
monotonically.
Or, add a "RefGood" function and a switch, so ref stays
at GND until core is lit up, then attach to the output
with only a RC-like profile (no whoop-de-do). This might
be more widely useful, let the system know not to do
anything with bad inputs.