In modern Taiwanese Min Nan, "tê" sounds more like "day" than "tea". Maybe it sounded different in the Min Nan of Fujian a few hundred years ago, or something was "lost in transcription" when the dutch wrote "thee".
My mums' native dialect is Teo Chiew, which is a variant of and falls under the Min Nan family of dialects (but can be quite different in many ways, a native speaker of one does not necessarily means mutual understanding of the others). And while similar, Teo Chiew uses a "dê” rather than "tê" for tea.
On another note, the area is also the origin of the "Gong Fu Cha" style tea ceremony. [1]
What kind of English accent do you have?
I'm from New Zealand, so the way I pronounce vowels is probably differs a lot from the prestige accents of English.
https://en.wikipedia.org/wiki/Help:IPA/Taiwanese_Hokkien
I have a hypothesis, mostly dependent on the position of a native English speaker, which I have no idea whether you are or not:
It's common to not be able to easily distinguish /e/ and /ai/. English does not have the former, and it tends to best match to the /ai/ diphthong, which glides over and would "average" to /e/.
It's also common to confuse aspiration and voicing on stops. English initial voiced stops are unaspirated, while initial unvoiced stops are aspirated. Hence, an unvoiced, unaspirated initial stop does not typically occur in English, and can vary in listener interpretation between /t/ or /d/.
This article covers voice onset time (VOT) and how voicing and aspiration play into it:
http://www.linguisticsnetwork.com/tutorials-aspiration-and-v...
Important note is that VOT is negative for voiced, near zero for unvoiced, and positive for aspirated. This measurable phenomenon backs up the fact that unvoiced, unaspirated sounds are basically in between standard English sounds and why you can get differing interpretations.
Not sure about the vowel sounds, I found those all reasonably trivial to distinguish.
https://mkdict.net/results?query=te%CC%82&page=1&q_type=tw&r...
If you click on the "+" button, there's a voice recording of how to pronounce it. It's from the Taiwanese Ministry of Education. To me it sounds much more like "day" than "tea".
I ran it by my wife, as she's a native Spanish and English speaker, and she agrees with /e/ over /ai/.
Thanks for that link. Very cool site; reminds me of dict.leo.org for German.
I can hear a slight difference between the vowel sounds in both tê and day. That's something I always just attributed to accent, not a different vowel - but I suppose vowel changes can be very subtle.
So maybe that makes it more obvious why it would be easy to confuse /e/ and /eɪ/, especially when your native language only has the latter. Brain heuristics work regardless of whether you want them to or not, and they'll fill in the missing /ɪ/ even if it's not present.