The operation of atomic clocks is based on the precise measurement of atomic oscillations, typically using the vibrations of atoms' electrons or nuclei. These clocks are highly accurate and are not affected by the type of vibrations you mention, which are quantum fluctuations associated with the electromagnetic field.
In the realm of quantum mechanics, particles and fields exhibit inherent fluctuations known as quantum noise. However, these quantum vibrations do not directly impact the functioning of atomic clocks in the way you describe. Atomic clocks rely on the stability and regularity of atomic transitions or oscillations to measure time accurately.
On the other hand, time dilation due to both special relativity and general relativity does affect the operation of atomic clocks. According to special relativity, relative motion between observers results in time dilation, which causes differences in the measured flow of time. General relativity extends this concept to gravitational fields, where clocks experience time dilation due to the curvature of spacetime caused by mass and energy.
The effects of time dilation on atomic clocks have been experimentally verified and are accounted for in their design and operation. In satellite-based atomic clocks, for instance, both special and general relativistic corrections are essential for achieving high precision.
While quantum fluctuations exist, they do not disturb the atomic oscillation filtering mechanism of atomic clocks in a way that affects their accuracy. The primary factors influencing the performance of atomic clocks are related to relativistic effects rather than quantum vibrations of the electromagnetic field.