Your Spring Arm component may be set to Relative Rotation rather than World Rotation. In your Character Blueprint, click on Rotation in Details panel and select Relative. Then make sure Use Controller View Rotation (under Camera Settings) is disabled. This should keep your camera rotation steady as your character moves around level.
Then in your Controller (or wherever you are setting Actor Rotation), make Target of your Set Actor Rotation node to Get Player Character. This will let camera keep its rotation while you rotate character.
My Controller Blueprint is set up like this:
