Within the Union of Soviet Socialist Republics, Kaliningrad was part of the Russian Soviet Federative Socialist Republic. As the Soviet Union broke up, each of its 15 constituent republics declared independence. Yes, even Russia. While Russia was the core of the Soviet Union, after 1990 it was led by Boris Yeltsin, who had little love for the Soviet multinational empire and wanted an independent Russia. One might say that Yeltsin played as much a role as Gorbachev in the breakup of the Soviet Union.

Anyway, as Kaliningrad had been part of Soviet Russia, after the breakup it went on being part of independent Russia. Not that it was a foregone conclusion that every piece of Russia would remain a part of it with the Soviet Union gone. Chechnya famously didn't agree, declaring independence in 1991 and only being brought back into the fold after 2 bloody wars. Tatarstan came close to declaring independence as well. But in Kaliningrad there were no ethnic issues to fuel secessionism. Most of the people to settle the region after World War II had been Russians. There were also some Belarusians and Ukrainians, but their numbers were much smaller and they tended to assimilate over time. So the question was, why would Kaliningrad not remain under Russian control?