I made the old trinket and then a new trinket on my Alchemist, and didn't get any errors with one equipped and one in my bag. Next I tried putting both of them in trinket slots. When you do this, you get the following error:
You can see the tooltip for the trinket has also changed to reflect this new system:
Note the "Unique-Equipped: Alchemist Stone(1)" designation. The previous version just said "Unique". So clearly a new category has been created for Alchemist trinkets to ensure that you only use one at a time. Either way, you can make extras and keep them in your bags for other gearsets. That's the important bit - multiple specs are being supported!
Another interesting Alchemy find I unearthed on the PTR was this little gem:
The Living Action Potion was previously sold by the Zandalar Tribe quartermaster and required Exalted reputation. As of today it will be a limited supply recipe sold in Everlook (Winterspring). Not a huge addition to the arsenal, but I'm glad to see evidence that some ZG items may be brought back to us.