Exactly the same has happend to me / our company.
I am using that chip for years now in our own SDR. But for the current production batch, we couldn't get hold on any Si5351A-B-GT (MSOP-10) anymore. So I was checking AliExpress as a last resort and ordered some samples from two sellers.
Before taking a closer look at them I simply soldered the first sample on a working SDR board (i.e. replacing the original SI5351A), just to find that the PLL would never lock. I used a scope to check the outputs and could observe exactly the same behaviour as described by @ebastler
Unstable, jitttering signal and periodical drop-outs. So I took the other sample from the second seller, same behaviour. Just to make sure I did not damage anything on the board, I took the original (desoldered) Si5351A and put it back in. Everything was ok again. Stable PLL reference and ADC sample clock.
So I decided to take a closer look. The top marking on both China ICs appeared to be the same as on the original one. But on the first China IC, the font was different. On the second chip, the font looked pretty much the same compared to the original, but the date code was reading 2xx (xx = two digits). 2 would mean either 2012 or 2022 and that doesn't seem to be correct.
Bottom line is, I am conviced that this is a China clone (not even scrapped genuine parts) and it's not worth the effort or the risk to make it work on our board.
During my research I found that there is an "official" China clone named MS5351M in an MSOP-10 package, that's how I discovered this thread. That clone is probably different from the Si5351 sold on AliExpress. I am not going to try it though. Instead, our company decided to buy "new old stock" from a reliable broker for 10 x the original price.