Explanation for behavior of acetic acid in aquaponic/hydroponic systems?
The source of the acid shouldn't matter much in adjusting the pH by a small amount.  What is the source of the calcium carbonate?  

If it is dissolved calcium carbonate only, as you might find in hard water, then this is strange.  The solution is buffered by the combination of dissolved carbon dioxide and carbonate minerals, so its pH might be difficult to change, but once it has been changed it should stay where you put it, more or less. 

If you have solid calcium carbonate (cement, limestone gravel, some pottery (notably not terracotta) or marble chips, perhaps), then what is happening makes a lot more sense.  You add acetic acid, lowering the pH and consuming some of the carbonate from the solution.  There is a large reservoir of carbonate available though, in the form of the carbonate minerals, and that eventually redissolves and the solution becomes more basic with time.