I am not an English teacher.
What Nietzsche means here is:
for all the world is accustomed to confound the author with his work. What there is of spirit, sweetness and goodness in the latter can evolve only over the years, [first] under the care of growing [reverence],then established [reverence], finally traditional reverence.
The sentence doesn't refer to "under the care of growing", but to "under the care of [...] reverence".
It is more understandable in German because of the peculiar German capitalization.
By the way, this is my first post on this message board. Cheers!
Student or Learner