According to the Statistical Account of Scotland (1796), Alva "is a part of the county of Stirling, though it happens to be totally disjoined from every part of it .... it is surrounded by the shire of Clackmannan on the east, south and west, and on the north, it is bounded by a part of the county of Perth".
The New Statistical Account (1845) repeats this information and adds, "Since the passing of the Reform Bill*, Alva has been politically incorporated with Clackmannan, but is still absurdly connected with the county of Stirling, for judicial purposes."
*1832 IIRC
So in 1796 and 1845 it belonged to Stirlingshire, but was mostly inside Clackmannanshire. It is probably one of the anomalies that was corrected in about 1890 when a lot of the more curious parish and county boundaries were rationalised.