That is unintuitive but correct behaviour.
Card text Inventor:
Gain a card costing up to $4 ■■■, then cards cost $1 less this turn.
Note that the time when you handle City-State (or other when-gain triggers) is marked in red, which is before the cost reduction happens.
So what happened was:
Buy Inventor#new_1
Use City-State to play Inventor#new_1
Gain Inventor#new_2
■ Use City-State to play Inventor#new_2
■ Gain Inventor#new_3 ■■■
■ reduce costs by $1 from Inventor#new_2
reduce costs by $1 from Inventor#new_1
<You may now buy more cards>
I marked the timing gap between gaining a card and the cost reduction happening in green for playing Inventor#new_1 and in red for play Inventor#new_2.
In other words, the cost reduction from the Inventors comes too late to be of use when playing a just gained Inventor.
Card text Inventor:
Gain a card costing up to $4 ■■■, then cards cost $1 less this turn.
Note that the time when you handle City-State (or other when-gain triggers) is marked in red, which is before the cost reduction happens.
So what happened was:
Buy Inventor#new_1
Use City-State to play Inventor#new_1
Gain Inventor#new_2
■ Use City-State to play Inventor#new_2
■ Gain Inventor#new_3 ■■■
■ reduce costs by $1 from Inventor#new_2
reduce costs by $1 from Inventor#new_1
<You may now buy more cards>
I marked the timing gap between gaining a card and the cost reduction happening in green for playing Inventor#new_1 and in red for play Inventor#new_2.
In other words, the cost reduction from the Inventors comes too late to be of use when playing a just gained Inventor.