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So far I haven't had this problem with any of my tarps and I normally run a CRL under the tarps. My new cloudburst is the exception since it has a slightly cat-cut ridgeline. I hear it doesn't sit well on top of a CRL so it's dangled beneath.
What makes the difference I guess is that the tarp is held in place with some small utility cord and a prusik or klemheist knot on each end. This serves to both hold the tarp in place on the CRL but also as a drip line. So far so good. Just leave the tail a little long so it helps to divert the water.
Good luck and stay dry....