Wikipedia's article on the Arctic Circle provides the explanation. Firstly, it says:
because the sun appears as a disk and not a point, part of the midnight sun may be seen on the night of the northern summer solstice up to about 50 minutes (′) (90 km (56 mi)) south of the Arctic Circle.
As the Arctic Circle is currently at roughly 66°34′N, this means a portion of the Sun is still visible on that night at around 65°44′N - the very latitude of the city of Kemi.
Another factor to take into account is the elevation of the viewing point. Kemi is not very high - just 4m above sea level - but it's likely there are higher points of land within the city, and tall buildings too. Greater elevation brings more of the Sun's disc into view.
UPDATE: the question was edited since this answer was posted, and Kemi was replaced with Kuusamo, "a city at 65°58′N" – which is further north than Kemi, and therefore would be able to see the midnight Sun for even longer.