The description on the TUFS site is accurate and the consonant used for つ is always the voiceless alveolar affricate. This sound also occurs in some languages such as German and Cantonese but many others, including Vietnamese and English, don’t have it and if you are not familiar with it you might want to spend some time practicing this particular sound. As for the video clip, I’ll go out on a limb and say the speaker has a slight tinge of a western Japanese accent (this is just an impression based on one extremely short video clip so I could be wrong) but that's because of a non-phonemic variation of the vowel “u” and the “ts” part has the same sound in almost all dialects of Japanese (at least the ones you will hear often). > Is there any chance that 'tsu' pronunciation varies among different contexts? There sure are a few sandhi rules associated with つ but it is never pronounced like “chu” unless the speaker is imitating baby talk or something.

Does not sound anything like ‘chu’ to me in the video. Perfect standard Japanese ‘tsu’.