As many species of Mantis exactly mimic sticks and leaves when motionless for purposes of defence, is it not possible that they mimic their surroundings for purposes of offence as well?
It is easy and natural to say that the Mantis presents a terrifying aspect.

It does to us, by association; but how can we say that it represents anything of the sort to the probably hypnotic or automatic consciousness of the cricket?
What does it really represent, as seen from below?
A twig, terminating in a bud, with two branching twigs growing from it, and a harmless nondescript fly or butterfly perched on the back of it.

The combination of a familiar sight and a threatening sound would very plausibly result in cautious immobility.

As for its instantaneous assumption of the pose, to move instantaneously is the next best thing to not moving at all.

It is less likely to startle than a slow movement.