I checked the log and your opponent did this "trick" on their normal turns 10 and 11.
They draw 3 cards at the end of each of those two turns, just as Outpost says: (the I is me on the reload)
[Turn 10]
...
I plays an Outpost.I plays an Altar.
I trashes a Copper.
I gains a Throne Room.
I plays 3 Silvers. (+$6)
I buys a Mission.I takes an extra turn after this one.
I plays a Night Watchman.
I looks at a Candlestick Maker and 4 Coppers.
I discards 4 Coppers.
I topdecks a Candlestick Maker.
I shuffles their deck.
I draws a Copper, a Silver and a Candlestick Maker.Turn 11
...
I plays an Outpost.I plays an Altar.
I trashes a Copper.
I gains a Throne Room.
I plays 3 Silvers and a Copper. (+$7)
I uses 1 Coffers. (+$1)
I buys and gains a Throne Room.
I buys a Mission.I takes an extra turn after this one.
I plays a Night Watchman.
I shuffles their deck.
I looks at 2 Throne Rooms and 2 Coppers.
I discards 2 Coppers and a Throne Room.
I topdecks a Throne Room.
I shuffles their deck.
I draws a Copper, a Throne Room and a Seer.About the contradiction that you see between Wiki and card, Outpost reads:
If this is the first time you played an Outpost this turn, and the previous turn wasn't yours, then take an extra turn after this one, and you only draw 3 cards for your next hand.
[emphasis mine]
As you can see it tells the player to draw 3 cards for their next hand, which happens at the end of the turn the Outpost is played (exceptions to this are rare edge cases). That's what the card says, and that's what happened.
The usual way Outpost works out that it is the only extra turn waiting to happen, so the 3 card hand you draw will be your starting hand in the Outpost extra turn. But this is not a usual situation, 2 extra turns are waiting for the same player, so they can decide which one goes first. And they smartly decided to combine the extra turn with the buy restriction (Mission) with the 3 card starting hand, to get a really bad extra turn and a really good one (5 card starting hand, no restrictions).
