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.
Er... No, I brain farted. The diphthong in "day" is /eɪ/. /aɪ/ (which I was listing as /ai/ on my phone) is as the word "tie".
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.
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.