This is a good question, which a scholar of international law would be more adept at answering. My answer is based on my own understanding of Estonia's modern history in particular, although many of the points also stand for Latvia and Lithuania (with the notable exception that these did not form a government-in-exile).

In 1939, the Soviet Union forced through a series of mutual assistance pacts in the Baltic states, allowing them to enter these states and begin a period of military occupation, practically ending two decades of independence. Subsequently, the Soviet Union rigged elections in the Baltic states, which gave them a legal pretext to continue their occupation, even though this was not recognized by the majority of western states. In Estonia, president Konstantin Päts was arrested in 1940 and sent in exile to a Siberian prison, where he would die several years later. In the years following, the Baltic states were at different times occupied by Nazi Germany and the Soviet Union.

In 1944, a National Committee (est. Eesti Vabariigii Rahvuskomitee) was formed in Tallinn, which sought to free Estonia from German control and re-establish independence, led by Jüri Uluots as acting president. As the year went on, it became increasingly clear that Estonia would not be able to regain de facto independence. At this moment, several members of the Estonian national committee fled to Sweden, whence the majority would later move on to Canada and the United States.

It is important to realize that although the Estonian government at this point was not able to regain territorial control, they still considered themselves to be the legal representatives of this country. This government, as well as many western states* did not recognize the Soviet Union's occupation of the country. It is not so unusual for different legal entities to claim governance over a single area: consider the Republic of China – Taiwan – and the People's Republic of China, both claiming full ownership over the Chinese mainland and the island of Taiwan.

To answer your question: Alexander van der Bellen was considered a citizen of the Republic of Estonia (represented by the government-in-exile), not a citizen of the Estonian Socialist Soviet Republic. These were two different legal entities claiming governance over a single area.

For further reading, you might want to check out Vahur Made's "The Estonian Government-in-Exile: A controversial project of state continuation" as well as Andres Kasekamp's A History of the Baltic States.