The fins are positioned way too low on the mast and should be adjusted up to a position where there is just a little play or looseness of the fin along the mast. I discovered some time back that too much slack allows the fin to drop on the mast which gives the bottom of the mast more opportunity to tear out of the fin.
IMO, this is not a fin adjustment problem, but likely a bent mast problem. A rearward bend on the mast will force the leading edge of the fin out along the mast.
On the other hand, fins should have some gap at the bottom of the masts to achieve the desired twist for good thrust. It's good to have about 1/4" to "wind up" the mast when the fins are static -- this gap disappears as you pedal.
Note also that all masts are not created equal. The early Turbo mast shown next on the far left is 1/4" longer than the others, extending the length of exposed mast significantly. Making assumptions based on the length of exposed mast, even if the mast is not bent, is risky.
Here is a fin that is properly set:
The clew outhaul is adjusted to keep the rear of the fin barely in the gap (about 1/8") so it doesn't pop out when twisted. Mast exposure is usually about 1/4" but can vary as noted above.
ANY touching of the fin end seems to cause an immediate tear.
If your fins are tearing near the bottom without provocation, take a look at the bottom edge of your masts. In the mast picture above, the first three have squared edges; the third in particular is likely to have burrs on the bottom from screwdrivers that can cut the fins from the inside. Only the fourth example (current mast version) has eased bottom edges. If you have any of the other mast styles, you can bevel the bottom edges with a metal file to make them smooth and easier on the fins. Hopefully that will solve your problem.