Do vertical stabilizers create vortices like wingtips do?
In general, the vertical stabilizer and rudder create a symmetric airfoil. As there is no pressure difference between the two surfaces of the vertical stabilizer, vortices doesn't form, unlike the wing, which is designed to produce lift at normal angles of attack (it is usually cambered, producing lift at zero angle of attack).
You're correct that the vortices are generated due to the movement of rudder. Usually, vertical stabilizer doesn't create vortices unless rudder is deflected.
Note: Though I can't be sure, I think the F-22 is braking (the F-22 does not have a dedicated surface for braking like F-15 and uses the normal flight control surfaces). A similar thing happens in the following figure

Source: f-16.net
Only one F-22 (second from top) is using its control surfaces, probably for braking, resulting in vortices from the vertical stabilizer.