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The transcription for <true> that you see in dictionaries is phonemic, that is, it's an abstract representation of the word. The phonetic transcription represents what happens in actual pronunciation and it would be like this ['t̠hɹ˳u] (superscript h). In this case, the place of articulation of /t/ is retracted because of /r/, so it is no longer alveolar but post-alveolar. /r/ is devoiced because of /t/ aspiration. They both form an affricate cluster, so as you say, the pronunciation is /tʃru/ rather than /tru/.
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