Picture 1 is a piston monostable pulse generator that works fine.
Picture 2 is the same piston monostable pulse generator that doesn't work.
The only difference between the two is how the redstone signal input to the pulse generator is created.
Picture 1's input signal is created by powering the redstone via a block that is powered by a lever. (note: this also works just fine if the input signal is created by powering the redstone directly, e.g. with a redstone torch or a redstone block or directly by a lever or basically anyway except the way described with regard to Picture 2).
Picture 2's input signal is created by powering the redstone via a redstone torch that is powered when the block it's attached to is un-powered by the lever. That is a complicated way of saying that when you un-power the block by switching off the lever, the redstone torch attached to it turns on, thereby turning on the redstone and creating an input (albeit an input that doesn't work in this case).
What I expected to happen was that the redstone signal input to the piston monostable pulse generator would behave the same way whether it was powered by a power component directly or by activating a torch by un-powering the block it's attached to.
To duplicate, you can replicate the redstone mechanisms from the pictures. They're only one wide and you can see everything (the pistons are sticky, but I imagine you could use regular pistons and gravity blocks, although I didn't try that).
For what it's worth, this mechanism functions the same way on iOS and XBox.