Simultaneous Machine Translation (SiMT) aims to yield a real-time partial translation with a monotonically growing the source-side context. However, there is a counterintuitive phenomenon about the context usage between training and testing: e.g., the wait-k testing model consistently trained with wait-k is much worse than that model inconsistently trained with wait-k' (k' is not equal to k) in terms of translation quality. To this end, we first investigate the underlying reasons behind this phenomenon and uncover the following two factors: 1) the limited correlation between translation quality and training (cross-entropy) loss; 2) exposure bias between training and testing. Based on both reasons, we then propose an effective training approach called context consistency training accordingly, which makes consistent the context usage between training and testing by optimizing translation quality and latency as bi-objectives and exposing the predictions to the model during the training. The experiments on three language pairs demonstrate our intuition: our system encouraging context consistency outperforms that existing systems with context inconsistency for the first time, with the help of our context consistency training approach.