When a relief pitcher is brought in with runners on base, the pitcher who let the runners reach base remains responsible for them if they score.
The run is charged to the pitcher who let the runner who scored reach base.
Whether it is earned depends on the other action in the inning.
ERA doesn't always reveal much about a relief pitcher's performance. A relief pitcher who often enters the game with one or two outs already recorded should have a lower ERA than a starter. The relief pitcher's effectiveness is judged less by how many runs he allows than by how well he prevents the inherited runners from scoring.