Tile is laid over heavy roofing felts with heavier membrane on the hips and ridges and flashing in the valleys. Tiles are secured to furring strips laid across the roof. A cracked tile will allow water to fall onto these subsurface layers and may result in leaking if they are not intact. Leaks tend to pool behind the furring strips and run horizontally until an opening allows it to drain downward.

Describe your roof (hips, valleys) and the type of tile (cement, stone, half-round). Rather than try to caulk this, you need to start looking for cracked tiles or one that has slid out of place. Most likely anywhere from the ridge down to above the point of leak. If you can look at the underside of the deck, you will probably see where the leak originates.

Tile roofs should be 100% waterproofed in the underlayments and flashing work PRIOR to the tiles being layed. Even if the leak can be traced to a broken tile, the underlayment "system" is deficient if that causes a leak.

A roof CAN be your friend