Why CMOS turns on when input voltage is zero?
Q1 is a p-channel MOSFET (aka "PMOS").

It turns "on" when the potential difference between its gate and source (\$V_{gs}\$) is negative. 

But where is its source connected? It's not connected to ground (in fact, none of its terminals are connected to ground). It's connected to Vdd. 

So what turns Q1 on is having the input voltage (its gate voltage) brought substantially below Vdd.

Since it has no connection to ground it doesn't "care" what the gate voltage is in relation to ground (i.e. whether it's positive or negative).