Going supersonic isn’t necessary to create a shock collar. And since it was in close proximity to people, you can guarantee the aircraft wasn’t going supersonic.
As the plane moves though the air, air in some places around the plane is accelerated in a way that it moves past the wings even faster than other parts of the stream. This is easier to picture if you think like an aerodynamicist, and consider the plane to be still and the air to be rushing past it (like in a wind tunnel). At certain points around the aircraft, the air will be going faster than in the “freestream,” which is the air moving far from the plane.
This acceleration can be substantial. At speeds near, but below, Mach 1, some of the air near the wings can actually are accelerated to greater than Mach 1. The aircraft might be moving at Mach 0.8 relative to the air as a whole, yet experience regions of airflow at, say, Mach 1.1 over the wings.
If some of the air gets going supersonic, it must shock itself down to subsonic at some point. Such a shock wave is the only mechanism by which supersonic flow can transition to subsonic flow. This shock forms somewhere over the middle of the wing (and/or fuselage), and is responsible for significant pressure changes in the air. These pressure changes cause the condensation you see associated with a shock wave if it’s humid enough.
The speed regime where this mix of supersonic and subsonic flow occurs around the aircraft is called transonic. You can tell the F-14 is only going transonic because the shock location is revealed to be in the middle of the aircraft. If it were emanating from the nose, that would be a sign that the plane was moving at supersonic speeds.
Now, it’s important to remember that this transonic shock is a very weak shock. It’s enough to condense moisture out of the air, but not to cause a sonic boom. That’s why it’s not a problem for the spectators. The bow shock ahead of a supersonic airplane is much much stronger, and its effects reach much farther from the source. The pressure spike associated with a shock like that is what causes sonic booms and broken windows.
In addition, a transonic shock isn’t the only thing that can condense the vapor out of the air. If it’s really, really humid, the drop in pressure associated with making lift can be enough to make clouds over the tops of the wings. This is more apparent during a high-G pull or other high angle-of-attack maneuver, when there’s some serious suction above the wing. This type of condensation is much less distinct, and more fluffy-cloud like. The shock-based condensation in Colophon’s link is a product of the humidity being “just right,” so that condensation occurs when the shock causes a pressure drop, but not at some lower threshold.