When you put two different items of the same level and quality into a premium fusion slot, one of them gets a free copy, so roughly two thirds of the successful fusions results should be the copied item (one quality higher). This is also what the cauldron shows before the fusion.
I did some tests with that setup and found that when the items were flawless or higher, then the results were roughly a 50:50 split
It's a significant amount of tests. The data rejects a "2:1"-spilt hypothesis with >99% confidence. Seems to be rather a 1:1 split (surprisingly accurately even in the test data), like the shadow copy didn't count except for the general fusion success chance (which looks okay for each of the qualities). And it doesn't seem to be related to a specific quality.
Something I briefly considered was the idea that the problem stems from cases where both items in the cauldron had equal worth, and that the fusion result from the server used a different copy. But even after eliminating those cases it was a 50:50 split (316 tests, 168 successes, 84 of them (50%) resulting in the copied item).
It's not quite clear yet whether this problem occurs when two great items are thrown into the cauldron. I only have a somewhat small sample of 37 tests here, with 24 of them (64.9%) resulting in a flawless version of the copied item. It looks like it might work properly here, but it's not conclusive given the small sample size.Edit:
Larger test sample suggests the same problem also for "great". See reply post.
It's also not clear if the problem is even related to the premium slot. It might as well be that a 2:1 fill of a regular cauldron slot produces a 50:50 split of results if successful. I don't have any test data on this. (Maybe someone else has?)
This should definitely looked into it. As players we need to be able to trust the fusion chances that the cauldron shows us.