Before you enter into that cave and talk to the person sitting inside, you gotta go through the hot springs area first. When you get there, there's a little area that you can have Cloud touch the springs. After doing that, head back to that secret cave and talk to the person you find. The person will get up and say something like "How dare you touch me with those filthy hands from the Hot Springs!" and you'll fight Snow. After you win the fight, the Alexander Materia will be on the ground where the person was sitting.
Hope this helps and good luck!
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