Something just hit me.
Getting from engineering to the bridge in a couple of seconds with the turbolift should be easy. If there is a turbolift tube going on in a straight line between the two, you can do it in about 10 seconds if you're accelerating with about 1g. All you have to do is apply artificial gravity of 1g in the direction of the acceleration, and voilą, you are having a smooth 10 second ride. And 1g should be easy for the gravity generators.
From there, getting the turbolift move slower as the plot requires it is easy. Not all rides will have a direct tube, and switching directions and tubes is slow. Sometimes there will be a lift in the tube already. Also, if I am wrong and gravity generation is ship-wide only, 1g and bigger acceleration might be available but used only in emergencies, and certainly this was an emergency.
Why would anyone complain about this?