You are on the right trail, I suppose. The database "Moi Krewni" (My Relatives) reports 31 Minkin persons in Poland, with their highest distribution in Wielkopolska (Greater Poland), and specifically: 11 Słupca County, 4 Koło County, 3 Konin County.
During the times of Poland's partitions the border crossing between Prussia and Russia was set between Strzałkowo (Prussia) and nearby Słupca (Russia). In 1915 Prussians build the infamous prisoner of war camp in Strzałkowo, which was also later used by Poland to keep there Soviet Union prisoners (war of 1919-1921) and since 1921 Ukrainian prisoners of war of 1920 with Ukrainian People's Republic. Strzałkowo is being used by Russian propaganda to counter Poland's demands for punishment of those guilty of Katyń massacre. Many POW died in Strzałkowo during typhus epidemic.
That said, Słupca must have housed some kind of Russian garrison, or at least some army barracks for Russian soldiers manning the border crossing. There is a defunct Orthodox cemetery in Słupca for Orthodox people settled in Słupca county in XIX century. At the spot of the former cemetery there is a monument commemorating the dead.
There used to be the Orthodox Church in Słupca, Poland, erected in 1914, but torn down in 1928, as a symbol of Tsarist / Russian domination. The second picture attached here shows unveiling of a monument on the Main Market in Słupca in 1926; The Orthodox church is seen on the background.

Orthodox monument in S³upca

Orthodox church in S³upca, 1926