Antivirals stop the formation of nucleocapsids and refurbishing of the cccDNA pool inside an infected liver cell. Therefore there will be an initial drop in both HBsAg(less cccDNA) and HBVDNA (less cccDNA + no capsids). After a while, only HBsAg will be produced by the remaining cccDNA.
N.B. This is my own thinking only, I have read no papers that say so. Watch the following diagram carefully, following the arrows. See which paths are blocked by antivirals. I don't have the text to the talk.