Do I still need a second cleanser after using an oil cleanser or balm?

In most cases, yes. The standard K-beauty and J-beauty approach is to follow an oil-based first cleanse with a water-based second cleanse to remove any residue. A handful of formulas in this roundup (notably DHC Deep Cleansing Oil) rinse clean enough that some reviewers use them solo in the morning, but at night, after sunscreen and makeup, a double cleanse is the consensus recommendation.