Is it always a direct and consistent connection? As in the animation flickers and then that crate has a rarer drop in it? Or is it more a general sense that if the animation is flickering you're going to get better results overall from that batch of crates?

If it's the first one it might be connected, if it's the second then almost certainly not.

I can always tell when I've successfully uncovered the bonus items in an antiquity excavation by making connections between the vents and then exploding them, because it will pause for a second or two before it shows the outcome. It doesn't make it any easier to find them of course, because it doesn't happen until I've already succeeded, but it means I know before the result is shown what's going to happen. I assume that's because the game needs a second to load the extra info after the explosion animation ends, whereas if I've found nothing it doesn't need to add anything.

There could be something similar with the crate animation. He throws out an extra card for the rarer items and I think they have a slightly different reveal animation, so if there's a bug related to those extra bits it could mean it flickers only when you're going to get something good. But it could also be a coincidence, or confirmation bias - you notice something strange is happening so you're looking out for different results.

(I never buy crates so I can't comment on the drop rate for the new ones, I only open the free ones from some events or login rewards.)