Huh! In my speech, the Tr in "tree" or "trigger" is really close to Chr as in "chree". In fact to pronounce "chree" I have to aspirate so hard to distinguish it from /tr/.
Is this common? [ˈt͡ʃɹi:] instead of [ˈtɹi:]? Why does this happen? Is there something about going from a plosive to an approximant that creates an affricate?
Long story short, yes, this is a very common way to pronounce the clusters /tr/ and /dr/. The reason why is that alveolar /t/ and /d/ tend to get retracted before postalveolar /r/ so that everything's in the same place of articulation; then because these retracted /ṯ/ and /ḏ/ sounds end up sounding like they're sort of "in between" alveolar /t/ and postalveolar /t͡ʃ/, many speakers will end up hearing them as /t͡ʃ/ and /d͡ʒ/.