The Mongols didn't administer Poland. The furthest they moved conquered in Europe (not battled, or advanced, but actually conquered) was modern day Russia. Due to internal politics their European conquest stopped short of Hungary and Poland, even though they did defeat armies of these kingdoms in battle. They didn't sack all the cities either. Their incursion was limited and due to complicated inheritance protocols and rivalry between grandsons of Ghengis Khan. Following victory over eastern Slavs, in total the Mongol empire spanned from China to Eastern Europe. These were still first generation Mongols who predominantly were from Mongolia and as such were relatively simple people with simple needs. With an Empire of such size, and complicated inheritence process, the priority for Juchi (Ghengis' son) (EDIT: It was even more complicated than that Juchi died, while quarreling with his father) was to stabilize his position within the Mongol state, not expand further not knowing if he will actually get to keep or profit from newly conquered lands.

Loosely interpreted from various sources, including Akunin's history of the russian state.

Mongols did not rule in Poland and afair nor in Hungary.

I don't know much about their wars with Hungary, but they showed up in Poland three times 1240-1241, 1259-1260 and 1287-1288. They would come, burn, plunder and rape and go home. No permanent arrangements made.