Well, Pozharsky was not a commoner ( he was a duke) and he didn't become a tsar. He was a leader of Russian uprising against Polish intervention. It was duke Mikhail Romanov who became the tsar.
First Polish intervention in Russian Time of Troubles in 1604-1606 and 1608-1613 was actually a private enterpise of some Polish magnats (Mniszech family) who tried to put an usurper Dmitriy on Russian throne. Second intervention in 1608-1613 also started as a private enteprise, later supported by some Polish troops. However, occupation of Moscow by Polish regular army happened even later. Tsar Vasili Shuysky (elected in 1606) allied with Sweden, which was then at war with the Polish-Lithuanian Commonwealth. Polish hetman Stanisław Żółkiewski crushed Russian-Swedish army in the battle of Kłuszyn, tsar Shuyski was overthrown by the boyars who offered Russian throne to Polish king's son Vladislav, if he converted to orthodoxy. Polish troops entered (peacefully!) Moscow and occupied the Kremlin. However, Polish king Sigismund III was fanatic Catholic, and he refused. Finally, in 1611 an anti-Polish uprising started and after long siege Polish forces were driven out of the Kremlin in 1612. In 1613 Mikhail Romanov was elected the tsar.