What does "simultaneously" mean in relation to a detonation shockwave? I understand that the difference between a deflagration and a detonation is that the reaction front of a detonation moves faster than the speed of sound in the material, which means that the pressure can not build up ahead from the moving front, so all the mechanical energy (is it impulse?) of the detonation arrives at the same time at the container wall, in form of a sonic boom.
But then, there is no such thing as simultaneous events in physics.
That's clear from computer scientists intuition, because it's just the same as in distributed network systems. 
So, while the sentence "The mechanical energy of a detonation arrives at the same time." sounds like ok on a shallow level, at the same time "at the same time" just does not make sense here. What does it even mean?

Is it like a layer of plasma, aligned in direction of velocity vector up to some pressure? 
Can the pressure be drived from speed of detonation front, mass and volume of reacted explosive?
 A: Background
The shock front -- the steepened, discontinuity in pressure, speed, density, and temperature (and magnetic fields if it's a magnetized plasma) -- is ahead of its driver, which is usually called a piston.  The region between is typically called the sheath (unfortunately, I couldn't find a quick article on sheaths for neutral gases).  An example of a sheath is very nicely illustrated in this article on bow shocks.  The thickness of the sheath depends upon the Mach number and geometry of the piston (and the magnetic field if it's a plasma again), which defines the stagnation point.  The change in fluid parameters are governed by the Rankine–Hugoniot relations.
The piston can be anything from a bullet to a planetary magnetosphere or even a jet of fast moving gas/fluid (as in astrophysical jets or the hot gas in an explosion).  The piston can move as fast as it is driven.  It will compress the fluid in front of it and create a sound wave.  If the piston is fast enough, generally above some critical communication speed like the speed of sound, the sound wave will steepen until it reaches a gradient catastrophe.  If sufficient energy dissipation exists to balance the steepening, it can reach a stationary state forming a shock wave.
Short Answer
The mechanical energy arriving at the same time is misleading here, but I think they are implying that the compressed, heated gas (i.e., the piston here) and shock wave arrive at roughly the same time.  In a neutral, collisional fluid (like the Earth's atmosphere) the thickness of the shock ramp is on the order of micrometers at STP and the sheath region would not be dramatically thicker (on macroscopic scales).  Thus, the shock wave and piston (which is your mechanical energy source) arrive at roughly the same time, but they certainly do not have simultaneous arrivals.
A: They are not simultaneous, but in most areas we can treat the margin of error as negligible. Therefore, they are approximately simultaneous. 
