Evolutionary algorithm hybridizing with A-means operation has been widely employed for data clustering. The A-means operation in this approach, however, is generally applied with a fixed number of iteration and at each generation (i.e., fixed intensity and frequency) during evolution, which could be far more than optimal. In this paper, we first introduce a generalized A-means usage framework, which can be used to arbitrary set the intensity and frequency of A-means operation. Based on the framework, we then propose a mechanism to adaptively control the intensity and frequency of A-means operation during evolutionary clustering process. To evaluate the proposed framework and mechanism, a series of experiments have been carried out on both simulated and real data sets. The results show that the proposed adaptive A-means operation usage is able to significantly enhance the performance of evolutionary optimized data clustering.