Check your AI Servo Priority setting. Looks like you could have it set to Release/Speed Priority rather than Focus Priority or Equal Priority.
AI Servo 1st image priority:
When starting to follow-focus a moving subject with AI Servo AF, if the user fully presses down on the shutter button immediately after starting to focus, what will the camera do?
Equal Priority: Camera allows a bit of time before firing first shot in a sequence, to give AF system a bit of "cushion" to focus completely on subject. This setting is new on EOS cameras.
Release Priority: Camera gives "priority" to releasing shutter – camera will fire virtually instantly, even if AF system hasn't fully locked-on to subject. News and wire-service shooters, who often are more concerned with the "decisive moment" than absolute tack-sharp images, may prefer this setting.
Focus Priority: Camera gives "priority" to assuring sharp focus – when trying to focus and shoot quickly, shutter release may be delayed for a perceptible moment while AF system confirms that first shot will be sharp.
AI Servo 2nd image priority:
This concerns what happens when the user tries to shoot a sequence of two or more continuous pictures of a moving subject with AI Servo AF. For the 2nd and all subsequent shots in that sequence, does the camera try to shoot as fast as it possibly can – even if this means a few frames may not be tack-sharp – or will it slow down the fps rate as needed to allow the AF system to confirm that virtually all frames in a sequence are as sharp as they can be?
Equal Priority: The EOS-1D X and 5D Mark III give equal priority to maintaining fps shooting speed, while allowing time for AF. In extremely dim conditions or with very difficult-to-focus subjects, shooting speed may slow down.
Speed Priority: Camera gives priority to maintaining fps shooting speed, even if it means the AF system may not have fully confirmed sharp focus for every frame in a sequence. Again, for example, capturing the moment may be more important for a traditional news shooter than having each and every frame tack-sharp in a high-speed sequence.
Focus Priority: During continuous shooting with focus-tracking in AI Servo AF, the camera gives priority to assuring sharpest possible focus for all frames in a sequence, and will readily slow-down the fps rate if necessary to allow this.