I'm not sure if I'm reading it and running it right.
Yes and No.
As written, the fact that there is no clue to the players or the characters that there is something they should be doing is unfair.
Generally, there should be something in the description that tells an astute player that they should look for traps AND/OR the characters should be allowed a passive check; the fact that both are disallowed is nor right IMO. All this does is train the players to search for traps everywhere which just bogs down the game.
I think you may not have played the first round right though. The players are surprised and one of them has "been dumped". Now this is not a fall that causes damage so our hero is not prone (PHB p.182).
The party is surprised, you should then roll for initiative. The odds are extremely good that the monsters will lose because their initiative bonus is appalling! Anyone with a +1 initiative modifier will win more than 75% of the time. If he wins, he loses his first turn and the monsters then attack, if he loses the monsters attack, he loses his first turn and the monsters attack again. However, depending where other party members fell in the initiative they may be able to intervene before the monsters' second attack.
Notwithstanding, I don't understand why the monsters had advantage on their attacks. The fighter is not prone, surprise doesn't give advantage and these particular monsters have no ability that gives advantage; so what am I missing?
Is it meant to be that lethal? How are they a CR of 1/4 each?
Well, there are 4 CR 1/4 monsters - a base XP of 50x4=200 x2 for 3-6 monsters = 400 - a deadly encounter for 3rd level characters.
Deadly. A deadly encounter could be lethal for one or
more player characters. Survival often requires good
tactics and quick thinking, and the party risks defeat.
So yes, I guess its meant to be this lethal.