You can tell that this one must be a loanword, because there are no original Vietnamese (and no Chinese loan-) words that start with /p/.
No matter how many times I listen it sounds like he is saying "Bean".
It's not really your fault. Vietnamese P, T, K/C/Q are unaspirated, which means that there is no puff of air coming out after them. If you pronounce the English word "pin", you could blow out a candle in front of your face, right. If you put your hand there, you will notice. Now say "spin" — you notice, (almost) no air coming out. That is the right sound. And if you pronounce this sound without the s- in front of it, it does sound a bit like "bin" (or "bean" maybe), because English doesn't have these unaspirated stops at the beginning of words.
I also thought it was "bin". This explanation is really helpful. I think the difference between the Vietnamese T and the English is that the Vietnamese T is aspirated, right? And the unaspirated sound is spelled Th in Vietnamese.
The other way round: Vietnamese th is aspirated (as in English top), while Vietnamese t is unaspirated (as in English stop).
Thank you! It is confusing because the "t" has a harsher sound, while the "th" sounds softer. But aspiration here makes for a softer sound. Since English does not have unaspirated stops at the beginning of words, both the "p" and the "t" are unfamiliar sounds to me.
Aspiration is the word for the "puff of air" that is coming out of the mouth after certain sounds. You can test it with your hand (or a candle) in front of your mouth. When you say "stop" (non-aspirated [t]), then only a little air reaches your hand or the flame, mostly from the following vowel. When you say "top" (aspirated [tʰ]), then you will notice a lot of air that might even extinguish the flame.
So actually Vietnamese t should sound softer. The word tôi should sound quite similar to "doy", while thôi would sound almost identical to English "toy".
To me it's a cross between a P and B. When I close my eyes and listen, it is clearer. That's what I do when I have trouble hearing a sentence. So far, the eyes closed method has worked on all but one so far.