Recently, semantic search has been successfully applied to E-commerce product search and the learned semantic space for query and product encoding are expected to generalize well to unseen queries or products. Yet, whether generalization can conveniently emerge has not been thoroughly studied in the domain thus far. In this paper, we examine several general-domain and domain-specific pre-trained Roberta variants and discover that general-domain fine-tuning does not really help generalization which aligns with the discovery of prior art, yet proper domain-specific fine-tuning with clickstream data can lead to better model generalization, based on a bucketed analysis of a manually annotated query-product relevance data.