Do I need to apply for a Korean Tourist visa?

According to Timatic, you do need a visa to enter the Republic of Korea, as well as evidence that you have to right to re-enter Japan (either stamped in your passport or the separate travel document issued to foreign residents).

Timatic is used by airlines to verify cross-border passenger documentation requirements. While perhaps not your carrier, Emirates has an easy and accessible search tool which you can use to check on your own.