The difference between the two sentences is that the first one is talking about a process that took place over a period of time (prices changing), while the second is talking about something that happened at a single time (someone moving).
When referring to a continuous process with details shown during a time period, "since" usually refers to the beginning of the period being described. If you show a graph with prices over a period of time, it would be unusual and confusing to say "since 1980" if the graph starts at 1990. While the start time given could be approximate (e.g. "since the 1980's"), there's no good reason to say a different time than the graph shows.
But when talking about a single event, "since" merely refers to some notable time before the event. In your second example, the time when someone left is an important starting time for a period, and the other event "they moved" happened at some time after that.
Note that even when you're talking about a continuous process, the first interpretation only applies if you're actually giving details. You can also make approximate statements like
Home prices have increased significantly since the 20th century.