If they sound great when plugged into your speakers, it sounds like they are outputting line level rather than phono level. Ah, yup, here from the FAQ:
“The RCA Outputs on the back of the TT250USB are Line Outputs and should only be plugged into Line Level Inputs. On your stereo, these inputs may be labeled as AUX, CD, or TAPE inputs. Do not plug the RCA Outputs into Phono Inputs. The TT250USB has a built-in preamp that will be too loud for Phono Inputs and will sound distorted or may cause damage.”
On your S4 where you’re plugging in your turntable, flip the switch that says “Line/Phono” to Line and it should fix your problem for you.