We present a general theory of noisy genetic oscillators with externally regulated production rate and multiplicative noise. The observables that characterize the genetic oscillator are discussed, and it is shown how their statistics depend on the externally regulated production rate. We show that these observables have generic features that are observed in two different experimental systems: the expression of the circadian clock genes in fibroblasts, and in the transient and oscillatory dynamics of the segmentation clock genes observed in cells disassociated from zebrafish embryos. Our work shows that genetic oscillations with diverse biological contexts can be understood in a common framework based on a delayed negative feedback system, and regulator dynamics.