I've also had tablet pieces appear after the rubble is cleared, but I did find most of the pieces while the villagers were clearing it.

Another thing you can keep an eye out for are the "bubbles" that appear with the collectibles, I guess as a little "hey, here I am in case you missed me". They don't bubble the whole time but the fact that they bubble at all has been particularly helpful to me when they appear behind a fruit tree, under the tree by the beach (where some take shelter from the rain) and when the color of the collectible is close to the color of the landscape where it's appearing.

Hope this helps!