Japanese writing and how things are pronounced are a little different. Phonemes ending with an "u" sound are by convention often the place holder for an unvocalized sound. Think a syllable boundary between two consonants in English. "Batman" would be written "Ba-tu-ma-n" in Japanese but still pronounced "Batman". For example in Paranoia Agent, the villain is always stated as "Shonen Bat", not "Shonen Batu", but the word "bat" here would in fact be written with the syllables "Ba" and "tu". Say "BAT" in English and notice that no matter what you do there's a slight hiss of air after the final "T". That slight exhalation of air is what the "u" in Japanese "tu" actually signifies. English also has that sound, we just don't write it down so we forget it exists.
This is a good explanation, but you unfortunately picked an example that's an exception and therefore wrong.
There is no "Tu" syllable in Japanese. It is replaced by "Tsu", and is never used to represent hard T sounds in loanwords. Instead, "To" is used. "Battoman" is how Batman is spelled, and "Shounen Batto". It's still generally voiced in a reduced way when they're trying to say an English word, though. D is a modification of T in Japanese, so the same goes for it. Bird = "Baado", Bed = "Beddo" etc.