What if it's not a powerfully enchanted item of magic, as is commonly assumed? What if the ancient builders were instead much more advanced than we give them credit for? The rest of the game is set in roughly 1000 a.d., so of course when we see something like that, we're used to assuming that it's magic. The idea is that what if it's an advanced redstone machine? Strong health-benefitting potions already exist, so this machine needs to monitor its holders health, which is why constant skin-contact is needed, and when it detects that a person has suddenly nearly died (heat sensors, fall sensors, sense for oxygen in blood, ...), it quickly stabs the holder with multiple small syringes with potions. The illagers obviously don't know that it needs to be held, so they simply keep one in a pocket.
Where the illagers found some is still unknown, but whatever the source, I find it highly unlikely that they'd know how to make any, as proven by the fact that they don't even know how to use them.