When its all over and done with you've got one of five sections for the star. Now the end of the toothpicks that are cylindrical are being apart and the water is being pulled down towards the leverage point thus providing a positive feedback loop for this separation. When the surface tension at the tip of the picks pulls the two tips together to close the gap, and the base of the cones (or bevels) touch to form a point of leverage, they over power the surface tension along the portion where the two cylindrical portions are touching. This point of leverage would be where the cylindrical portion of the toothpick ends and the bevel begins.
The second thing that the bevel provides is a point of leverage along the length of the tooth picks. This is because the bigger gap forces the surface of the water to be more stressed out and thus want to pull its self back together again, where as on the cylindrical parts of the toothpick the surface tension of the water is more relaxed since the toothpicks are already touching. First it creates a higher surface tension than an equally long section of side by side cylinders would (aka the un-beveled parts of a toothpick). The bevel of the toothpicks used to create the pointy side makes a triangular gap when two toothpicks are side by side or parallel to each other. When they spread out again to form the star theres some more complicated shit at play. At first slowly and then faster and faster with capillary action. Surface tension of the water pulls the tooth picks together at the base of the toothpicks.
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