I would say that depends whether the earlier civilizations were present immediately before the borrowing civilization, so the two could have contact, or were separated by a long period of time.
If a civilization borrows from a civilization just was there shortly before, and that they possibly invaded, the borrowing might happen not on purpose, but be a result of a natural mix and inclusion of what it already there. Alternatively, especially when a new power wants to assimilate local population, they might want to include elements from their previous culture to ease the transition for them and make it more acceptable (e.g. the Virgen og Guadalupe in Mexico, although a Cristian Deity, borrows greatly from pre-colombian civilizations.)
If a civilization borrows from an older one, it might be to evoke an association with them, as when Europe borrowed from the Greeks and the Romans, when they wanted to break with the association of the Dark Ages in the Renaissance and instead "go back to their intellectual roots"
