The fear is based on receiving more objective evidence that Russian leadership desires to expand its influence to more closely match the geographic reach previous Soviet and Russian empires.
While there have long been people (and sometimes leadership) in Russia saying that neighbouring countries and perhaps Eastern Europe belong or should belong to the Russian sphere of influence, much as they did in the days of the Cold War, it's not unreasonable to dismiss this as just nationalist talk, particularly when the statements are intended for domestic consumption within the country.
Actual invasions are a different thing, however. The invasion and takeover of Crimea could be dismissed as Russia needing to keep its (strategically very valuable) naval port in Sevastopol, but the subsequent invasion of Ukraine and attempt to take the capital make it clear that Russia's declared intent to exercise significant control over nearby countries is more than just talk.
If Russia manages to exercise control over Ukraine (or perhaps even if not), the next obvious targets in a westerly direction are the Baltic states since they are close (two border on the main part of Russia itself; the third borders on Russia's exclave Kaliningrad and Belarus), small (Lithuania has a population of less than three million, and the other two less than two million), and were part of old Soviet empire. Estonia and Latvia still have a significant (20-30%) number of ethnic Russians in their populations. ("Protecting" ethnic Russian minorities has been used as a reason, pretextual or not, for Russian military actions in the past.)
These characteristics make them not only plausible targets for empire expansion, but also, because they are small and "distant" members of NATO, good tests to see how how serious major NATO countries are about coming to the defense of any member that is attacked, even if it involves fighting against another nuclear power.
Note that, because of the "why was there no such fear before?" part of your question, I have assumed you are talking about "Western" countries, and not the Baltic states themselves. Estonia, Latvia, Lithuania, Poland and probably several other countries in the neighbourhood have had no opinion change at all about Russia: the have always considered Russian imperialism to be a great danger to them, a fear amply justified in their eyes by hundreds of years of history. This is why they scrambled to join NATO as quickly as possible after the fall of the Soviet union. It's just more western countries that recently took a while to come around to their point of view.