From Wikipedia, emphasis by me: “The rising level of the Caspian Sea between 1994 and 1996 reduced the number of habitats for rare species of aquatic vegetation.” Now that doesn't actually answer your question (it could be an exception to a general trend), but together with no mention of a general size decrease mentioned in that article as far as I can see, it hints against the Caspian Sea shrinking as a general trend.

The Aral sea (actually a lake) shrunk because the rivers that fed it were diverted for a Soviet irrigation project in the 1960s. This was an unusually large-scale project with an unusually drastic result. I gather from Wikipedia that water is extracted from rivers feeding the Caspian, but they haven't been entirely diverted so if there is any shrinkage due to industrialisation it is unlikely to be on a comparable scale.