Rising edge of a pulse or one complete pulse needed for 1 step in Stepper motor?
I'm confused as I'm not able to figure out when common stepper drivers
  executes a step, whether at the rising edge of pulse sent by
  controller or falling.


For the Allegro A4988 I would refer you to figure 3 in the data sheet: -



Following activation of a "step" command, it looks to me like the load current is changing on the leading edge i.e. pretty much instantly. There are other pictorial examples in that device's data sheet that confirm this.

For the DRV8825 it's a similar story: -