Recently there has been significant progress in the field of dialogue system thanks to the introduction of training paradigms such as fine-tune and prompt learning. Persona can function as the prior knowledge for maintaining the personality consistency of dialogue systems, which makes it perform well on accuracy. Nonetheless, the conventional reference-based evaluation method falls short in capturing the genuine text comprehension prowess of the model, significantly relying on the quality of data annotation. In contrast, the application of metamorphic testing offers a more profound insight into the model's distinct capabilities without necessitating supplementary annotation labels. This approach furnishes a more comprehensive portrayal of the model's intricacies and exposes intricacies concealed within reference-based validation techniques. Consequently, we introduce a persona-centric metamorphic relation construction for metamorphic testing, aimed at evaluating both the persona consistency and robustness of personalized dialogue models. For that reason, this work evaluates several widely used training paradigms including learning from scratch, pretrain + fine-tune and prompt learning in personalized dialogue retrieval to know if they are more robust or if they have the same flaws as their predecessor. Under three kinds of designed metamorphic relations with consistent outputs, our experimental results reveal that prompt learning shows stronger robustness compared to training from scratch and fine-tune. Although tested retrieval models gain competitively high retrieval accuracy according to the traditional reference-based validation, they are still fragile and demonstrate various unexpected behaviors, thus there is still room for future improvement in personalized dialogue retrieval.