Since this is non-terminal the 'penalty' only hurts in edge cases, since it isn't particularly useful for the opponent can just play it on their turn. I'd make it terminal, then it could work. Even as a terminal it feels a bit strong because it is a non-terminal smithy next turn at a cost of 3, and that not even considering the sifting. You're probably going to call this next turn almost everybtime anyway, so I'd make it a duration maybe, though you would have to change the penalty.
It does allow them to call the card a turn sooner, but that is still probably not a big enough drawback (except possibly for the version that gives other players +1 card if they put a reserve on their mat). I agree it would probably be better as a terminal. I guess I was reluctant because my only other reserve card (Illusionist) is terminal coin on play, and I don't like it to do nothing at all on play.
Bartender
Cost $3 - Action / Reserve
+$1. Each other player may put a Reserve card from their hand onto their tavern mat. Put this on your tavern mat.
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You may call this at the start of your turn for discard 2 cards, then draw 4.
Also, I don't think you'd always be calling this the next turn after you play it because you could easily not have two cards you'd want to discard to draw more (especially if you've been hit by a discarding attack). Partly for this reason, I'm leaning more toward the discard first, then draw rather than draw and then discard -to keep it from being too strong for a $3 with a minor drawback.
...OR I just had an almost-completely different idea which is close enough to the general concept* to take the name:
Bartender
Cost $5 - Action
+1 Card. You may put any action card from your hand onto your tavern mat. If it isn't a reserve card, at the start of your turn, you may call that card for its usual on play effect.
I'm wondering if there will be enough interesting uses for this for it to be a good reserve card. And by 'interesting', I mean not just using it as a splitter or something that may as well be a duration. Also wondering if it'd be better if it said "any action card costing up to $4".
*I guess the general concept really is a card that puts other cards on the tavern mat. Maybe this general idea will split and become more than one card.