Your implementation is really close - on the website, here's the diagram that they used:
So, I think you reversed the angles - it should be $-\pi/2, -\pi/4, -\pi/2$. (Also: there's a QFT inverse that Quirk has, so you can verify that the first half of your circuit is correct).
Quirk uses the convention that the top qubit is the least significant qubit. When Quirk shows the ket $|001\rangle$, the rightmost bit (the 1) is the top qubit line and the equivalent decimal value is 1 (instead of 4). This is the opposite of the convention in Nielsen and Chuang.
Basically this means that, in Quirk, it's the top qubit that should control the ...