First of all, you were right to ask this question. Obviously, you’ve heard how native speakers really talk. My advice is that you listen to what native speakers really say, not what they say they say — unless they’re experts on English phonology. You are absolutely correct — the first T is not given its full pronunciation before another T. In my experience, when Chinese people attempt to give it its full pronunciation, it tends to add an extra syllable, and usually destroys the natural English rhythm. So, here’s what you do to sound like a native: “contribute to” 1. make the beginning of the first T by simple stopping the air flow. This is the first T — an unreleased T. 2. pause briefly 3. release the T (this serves as the “second” T. Essentially, you get just one T, with a slight pause between the stop and the release. “complete the” In order to combine a T with a following voiced TH, the process is similar, however, the T will be with your tongue touching your upper teeth (in preparation for the TH), instead of your alveolar ridge. The release will be unaspirated, i.e. with no puff of air (this may sound like a D to a Chinese speaker, although it is actually an unvoiced T). Alternatively, if you want to sound very “proper,” you can pronounce an unreleased T and then release just enough to produce a TH sound at the end. The TH sound, while phonemically (theoretically) voiced, will probably be phonetically unvoiced (assimilated to the unvoiced T sound) in actual practice — that is normal. Again: listen to what native speakers really say, not what they say they say.

No, both t's are pronounced

They are pronounced, but held. So you say "contribute_to", not "contribu-to". In the first example, t and th are different sounds. You shift from t to th by moving your tongue forward.

It's because I couldn't distinguish it by listening the English learning materials.

What made you ask this question? I'm just curious.