Do adrenal tumor symptoms happen at any time of day?

Sometimes: The most common adrenal hormone is cortisol. This hormone has a "diurnal" or morning-evening variation. This variation is lost when there is a tumor producing this hormone, since a tumor is unchecked growth and therefore does not come under the usual control of other feedback methods.

Yes: Hormonally active adrenal tumors like pheochromocytoma or a cortisol producing tumor are capable of producing symptoms at any hour.