The presence of skew causes a correlation between volatility and spot. This correlation produces a negative shadow delta for all forward starting products (forward starting options have a theoretical delta of zero).
How does this produce a negative shadow delta? The exact mechanism is not clear to me.
Basically, the author is saying that the delta of an option,
$dC/dS = \frac{\partial C}{\partial S} + \frac{\partial C}{\partial v}\frac{\partial v}{\partial S}$,
where the $\frac{\partial C}{\partial S}$ is the delta assuming constant volatility, the $\frac{\partial C}{\partial v}$ is the vega of the option, and the $\frac{\partial v}{\partial S}$ describes how the implied volatility of the option moves as the spot price moves. This second term is the "shadow delta" being referred to.
