/ðiː/ before words begin with a vowel sound: the American people the onions the egg /ðə/ before other words the man the girls

Before a vowel sound, it's far easier to say /ðiː/ than /ðə/. Try it. ^^ Does that match with your recording as well? :)

It doesn't sound odd to just use whichever you want. They are the same.

I tend only to say /ðiː/ for emphasis, and /ðə/ for all other cases, but that might be a British thing.