The direct-speech brain-computer interfaces (DS-BCIs) with self-paced paradigms are much more promising and practical than indirect BCIs with general synchronous paradigms. As the exact onset and offset locations of analysis window are hard to achieve in the imagined speech of ideal DS-BCIs, spoken speech with clear audible output in this study is used as a medium to study the impact of exact location of analysis window in self-paced BCIs. This work aimed to use shifted analysis windows to simulate the situations with different levels of onset location errors of analysis window in the EEG-based classification of spoken Mandarin monosyllables carrying vowels and lexical tones. The analysis window (based on the duration of the available overt speech) was shifted from the true onset location. The Riemannian manifold method was used to extract features for the collected EEG signals, and a linear discriminant analysis (LDA) was employed to classify different vowels and lexical tones. The results in vowel and tone classifications were 70.7% and 54.9%, respectively, at an overall best-shifted level. It was found that vowel and lexical tone classifications reached their best performances at different shifting levels of analysis window. When choosing a suitable analysis window, the EEG signals without shift were more suitable to classify vowels, and those EEG signals away from the onset location were found to benefit tone classification.