B757-200 IOE CHK CAPT; DSNDED BELOW CHARTED RECOMMENDED ALTS ON THE RIVER VISUAL APCH TO DCA.

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FLYING THE RIVER VISUAL APCH TO RWY 19 AT DCA AIRPORT; OUR ACFT WENT BELOW THE RECOMMENDED ALT ON THE PROC. NOT SURE IF ANY TECHNICAL RULE WAS VIOLATED. HOWEVER; UPON SWITCHING OVER TO TWR FREQ; THEY ASKED US TO CHK OUR ALT. THE CAPT BRIEFED (DISCUSSED) THE APCH PROCEDURES; PRIOR TO THE LOCAL AREA. HOWEVER; AT 10 MI OUT; AND CLRED FOR THE APCH; HE RUSHED THE AIRPLANE TO DSND. NOT SURE WHY HE WAS DSNDING TOWARD; AND PAST; THE RECOMMENDED ALTS ON THE CHART. I POINTED TO OUR DME; AND TOLD HIM HE WAS LOW. HE CONTINUED TO DSND. BECAUSE IT WAS A VISUAL APCH; AND THE CHART HAD RECOMMENDED ALTS; I VOICED MY CONCERN AGAIN; BUT DID NOT PRESS THE ISSUE; AS THERE WAS NO DANGER YET. PASSING THROUGH 1400 (AGL) WE SWITCHED TO TWR. TWR WARNED OF OUR ALT. AT THAT POINT HE LEVELED OFF AND REALIZED HE HAD DSNDED EARLIER THAN NORMAL. IT WAS MY FIRST LEG ON THIS AIRPLANE. THE CAPT WAS GIVING ME A CHK RIDE. MAYBE HE DISREGARDED MY WARNING BECAUSE HE ASSUMED I WAS INCORRECT. DME CAN BE CONFUSING IN THIS AIRPLANE; AND I BELIEVE HE WAS POSSIBLY LOOKING AT DME ON THE HSI OR CDU; INSTEAD OF THE TUNED VOR.