Hi, Anonymous. "Visit us" doesn't actually sound as "Visi tas". In the English language, native speakers use neutral sounds called the schwa. It is a neutral sound - not silent. The schwa sounds like "uh". You would then say those words like "Vizi tuhs".
The /t/ sound moves toward the third syllable by the phenomenon of liaison: there is a tendency for sounds to be grouped as consonant + vowel, and here we get vi + si + tu + s.