FWIW it’s a myth. A mushroom cloud is disproportionately big for the actual blast radius, so the cloud could be bigger than your thumb and you might still be a safe distance away from the blast (though not necessarily from fallout)
Also, the largest deadly blast radius for a nuclear blast is the thermal energy, which cooks anything within a large area at basically the speed of light. So if you’re within the “danger” radius that the thumb trick would supposedly tell you about, you’d already be vaporized before you could lift your arm.