As per title Hirschgeist invulnerable during both day (as intended) and night when summoned with the hand of fate

This is true and sometimes you cant damage it even at night.
But, you can still kill it with AOE damage weapons, like Harming potions:

Ok, seems like invulnerability of Hirschgeist is "feature" of Better Animals Plus Plus and i just need to add more information about it in quest book.