When does a UNIX directory change its timestamp

The timestamp is updated when the data that represents the directory changes. A change in a subdirectory of directory D does not change anything in the representation of D because D only points to the subdirectory, not to what's inside it. On the other hand, creating a file in D changes the block of data on disk that represents D.

A directory's timestamp is changed when the Directory itself is changed. The directory contains, among other things, a list of the inodes of the files in the directory so when you change the content of the directory by adding or removing files then the Directories timestamp will be updated.