A C172 INSTRUCTOR AND STUDENT DESCENDED PREMATURELY AT KISM; CAUSING A 'MINIMUM SAFE ALTITUDE WARNING' TO BE ISSUED BY TWR.

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I WAS ON INSTRUMENT TRAINING FLT WITH ONE OF MY STUDENTS. WE WERE PROCEEDING ON A VECTORED APCH FOR NDB 15 APCH INTO KISM. WE WERE IN CONTACT WITH ORLANDO APCH. MY STUDENT HAD TUNED AND IDENTIFIED THE ORLANDO VOR AND HAD ALSO SET UP OUR 'OBS' SELECTOR FOR THE 211 DEG RADIAL OFF ORLANDO VOR IN ORDER TO IDENTIFY A STEP DOWN FIX (VINYL INTERSECTION). WE WERE INBOUND ON THE APCH OUTSIDE OF VINYL (I BELIEVE WE WERE APCH 800 FT MSL) WHEN ORLANDO APCH TOLD US TO CONTACT TWR. WE ALSO HAD ISM IN SIGHT AT THIS TIME. AS WE CONTACTED ISM TWR; OUR VOR NEEDLE CENTERED. AS WE BELIEVED WE WERE OVER VINYL; I BELIEVE THAT WE MIGHT HAVE STARTED OUR DECENT TO MDA (AS I RECALL; THE STUDENT PERFORMED A FEW CHECKS BEFORE STARTING THE DESCENT. ISM TWR ISSUED US A 'LOW ALTITUDE ALERT;' BY THAT TIME IT APPEARED AS THOUGH WE WERE INSIDE OF VINYL INTERSECTION (DUE TO VOR INDICATIONS); THOUGH VISUALLY THE DISTANCE TO THE ARPT APPEARED TO BE APPROX 6-7 MILES. APPROX ONE MINUTE AFTER THE 'LOW ALTITUDE ALERT;' THE CDI NEEDLE ON OUR VOR INDICATOR APPEARED TO RE-CENTER. AND WE PROCEEDED THE APCH VISUALLY. I AM NOT SURE IF THE SITUATION CAME ABOUT DUE TO HUMAN FACTORS OR MECHANICAL/RADIO PROBS. THOUGH BOTH PLTS RECALL THE CDI NEEDLE CENTERING TWICE; BETTER SIT AWARENESS WITH VISUAL REFERENCE MIGHT HAVE HAD A POSITIVE EFFECT ON THIS SIT. I AM NOT SURE IF ANY VIOLATION OCCURRED DURING THIS APCH.