In the scene where Tamina tells Prince about the passageways underneath the city , which lead to Sands of Time . She also mentions there if the move fast enough they can reach the hourglass before Nizam . Later she locates and press a hidden switch that opens a passage for easy access to hourglass . When the scene rolls we are able to see a small stone falls from roof and hit the down the entrance and then run down ( the scene of stone hitting surface is not shown ).
Tamina instructs that the is just one safe path toward entrance and nothing else can touch surface other that where she steps.
But later we can see prince saving a big rock from hitting sand ground and then a small stone hit ground which causes the whole floor to turn into sand and prince falling in quick sands .
Well this creates some wrong directions as the surface must had been start falling since the stone touch ground even before Tamina pressing key for correct path