SMA ARRIVES AT 31J AFTER TWR WAS SUPPOSED TO CLOSE AND FOUND TWR STILL OPERATING.

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ENRTE TO LAKE CITY ON A VFR INSTRUCTIONAL XCOUNTRY. ACCORDING TO THE ARPT FACILITIES DIRECTORY; LAKE CITY TWR (NFCT) CLOSES DURING THE WK AT XA00 LCL. UPON REACHING THE ARPT AND OBSERVING NO TFC IN THE PATTERN WE POSITIONED OUR ACFT FOR A DOWNWIND FOR RWY 10. MY STUDENT MADE A RADIO CALL FOR DOWNWIND ON THE LISTED UNICOM FREQ OF 122.7 LCL TIME WAS XB00. A VOICE WAS HEARD TO USE THE CTAF OF 119.2 AN ERROR I HAD NOT CAUGHT EARLIER. AFTER CHANGING THE FREQ AND MAKING ANOTHER DOWNWIND CALL. HOWEVER THIS TIME WE RECEIVED A CLRNC TO LAND FROM THE LCL CTLR OF THE STILL OPERATIONAL TWR. 1 HR AFTER THE LISTED CLOSING TIME OF XA00 LCL TIME. NO NOTAMS WERE ISSUED FOR THIS CHANGE IN OPERATIONAL HRS. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: SPOKE TO FSS AT GNV. HE SAID THAT THE HRS PUBLISHED IN THE ARPT FACILITY DIRECTORY ARE CORRECT. HE SAID THAT; AT TIMES; THE TWR WILL REMAIN OPEN FOR A SHORT TIME PAST THOSE HRS TO ACCOMMODATE A MIL ACFT ARRIVING AT THE CIVILIAN CONTRACTOR FACILITY. IN THOSE CASES; THE PROC IS EXACTLY AS HAPPENED TO THE RPTR; THE FBO MONITORS UNICOM AND TELLS ANY TFC TO MAKE A CALL ON CTAF FREQ; THE SAME AS THE TWR.