Technology

Depends on how it is fulfilled, if it comes from an Amazon warehouse directly vs directly fulfilled by a third party (if it comes in an Amazon branded box with Amazon tape it probably got fulfilled at an Amazon warehouse).

If it did get fulfilled at an Amazon warehouse, the one I worked at it goes through a process wherein it is retrieved either by a "picker" manually or via a KIVA bot filled with items (depends on how old the warehouse is, I'd be surprised if they're not all converted to KIVA bot style by now as it's been nearly ten years since I've worked there and I worked in a brand new warehouse at the time and we had the bots style)

So the picker puts it into a bin with several other items all scanned together using the ASIN number (separate Amazon barcode, longer and shorter then other barcodes) which gets loaded onto a conveyer which eventually ends up at a sorter, if it's AFE (multi-item orders, the department I mostly worked in) it gets pushed to a certain line where it's manually further sorted from the yellow bin, scanned again and placed into a smaller grey bin (rebin) which goes to another sorter eventually into another line where it gets placed into a wall of cubby-holes (I believe that was called induction), the cubby holes would have all the items for an order, once it's "complete" you push it through to the other side of the cubby hole where the packers are, the packers have a screen that tells them what items are in the order, along with which box to use, they have a whole wall in front of them of different box sizes, along with a feed of the larger bubble cushin things and an automatic tape dispenser for the box side the system told the packer it needed (it didn't work a lot of the time so there were also buttons to select a specific box size of tape).

After all that the packer pushes it forward into another conveyer belt, where it is weighed automatically to hopefully ensure it is correct, if it is close enough to the correct weight, it goes out to shipping. (If not, it gets kicked out for problem solvers to figure out what's wrong with it, that was my main job).

Single item pack is less complex slightly for obvious reasons (don't have to stage the items together) but is the same basic idea.

Now to answer the questions specifically, why a small bottle of vitamins ends up in a large box, either they ran out of the correct box needed or it was just an incompetent worker who doesn't care what box they use regardless of what the system tells them they should use. Technically the system could kick it out, but that's a lot of extra time, effort and a wasted box.