A Kriging-assisted Reference Vector Guided Evolutionary Algorithm (K-RVEA) is one of the most successful surrogate-assisted multiobjective evolutionary algorithms (SAMOEAs) for solving expensive multiobjective optimization problems (EMOPs). In K-RVEA, an evolutionary search algorithm is conducted on Kriging models approximating objective functions, to identify better solutions while saving the expensive function evaluations. Thus, the maximum number of generations for this model-based search process is crucial in improving the performance of K-RVEA. Although many works have attempted to improve the K-RVEA framework, there has been little attention in this regard. Accordingly, this paper proposes an extended K-RVEA that can adaptively select an appropriate number of generations for the model-based search process. To this end, this paper starts by conducting an analysis to understand an effective strategy to improve the K-RVEA performance in terms of the number of generations. Subsequently, we introduce an adaptive selection mechanism based on the analytical results, and integrate it to the K-RVEA framework. Experimental results on benchmark problems in their multi/many-objective settings reveal that our extended K-RVEA outperforms the original K-RVEA on many experimental cases.