Is it known whether the behavior of companies storing consumer data and transmitting them over the Atlantic has changed so far?
Mostly no, see e.g. Facebook's response to a demand and summons letter. There is a period of grace until January 31, 2016, and chances are a new agreement to replace Safe Harbor will be worked out until then – otherwise that is when there will be visible changes.
Never the less, big companies are increasingly building or expanding European data centres, e.g. Microsoft, Amazon and HP give customers the option of storing data in Europe.
If you take a look at the certified Safe Harbor companies, however, it becomes obvious that the dark figure of (smaller) companies storing data in the US must be way higher – but since they have operated illegally up until now, they're likely to also do so in the future, depending on how rigorously the data protection authorities will enforce.
Update 02/03/16: Privacy Shield will be the new agreement, based mainly on US guarantees to not give their intelligence agencies indiscriminate access to EU data.