Hi Audrey,
You’ve picked up on one of the effects of what is known as coarticulation, or how a neighboring sound can influence another’s pronunciation. This occurs with relative frequency. For example, the vowel in the name Sam sounds quite different from that in the word sat, even though both are allophones of the /ă/ phoneme. This is due to the nasalization of the /m/ consonant immediately following the vowel in the name. In anticipation of this sound, our soft palate moves somewhat preemptively, nasalizing the vowel sound as well.
Consider the phonemes that the letters in your example represent. When producing the /t/ and /d/ sounds, we use the tip of our tongue along the alveolar ridge, right behind our top front teeth. Now produce the /r/ sound. While there are variances in how people shape their tongue for the /r/ phoneme, the tongue is generally pulled towards the middle or back of the mouth, possibly bunching the tongue body. This tongue positioning might approximate how you make a /y/ sound, particularly in the lifting of the tongue body. Because the movement is so large and drastic from the alveolar /t/ and /d/ sounds to /r/ or /y/ sounds, we often begin to shape our tongue for the first phoneme in a way that more closely approximates that which it must take for the second phoneme. So, the /t/ sound may become a /ch/ in words like train (“chrain”) or phrases like got ya (“gotcha”). Similarly, the voiced counterparts of these phonemes may make words like drink sound like “jrink” and did you becomes “didju.”
Variations in how we speak are perfectly natural and expected. We all have different influences on the dialect we speak for many reasons, such as our culture(s), regions we have lived in, and our generation. Our speech also may be influenced by coarticulation more or less than others. None of these variations of oral language are “right” or “wrong” or need correcting. Less variance is accepted when spelling, however. While we do acknowledge some regional spelling differences (e.g., color/colour), it is most often anticipated that we spell words consistently across a language. This means that even if a student pronounces the word as /chrē/, they must learn how to spell it as <tree>.
If you notice these types of misspelled words from your students, it’s helpful to acknowledge that theirs was a perfectly understandable spelling attempt, because we do often hear this word pronounced as /ch…r…ē/. It may or may not be helpful to add that the letters <ch> represent /k/ when followed by <r> (as in Christmas and chrome) or that <jr> is not an acceptable letter combination in English. Either way, you can continue your redirection with something along the lines of “There's another way to pronounce that word, too. Listen carefully.../trē/. That's actually the way we spell it, as /t...t...trē/.”
All that and I still haven’t actually answered the question that you asked! As someone who grew up in the South to Midwestern parents but has lived most of her adult life in California, I have had many dialectal influences on my speech and oral language. As such, I can never commit when asked directly how I pronounce words like caramel, pecan, or crayon. I’m convinced I say them differently on different occasions, and I think my pronunciation of <tr> and <dr> words is also variable based on the day or context as well. If I’m saying the word in isolation for a student to spell or identify on a vocabulary test, I would most likely pronounce the initial phonemes as /t/ or /d/, respectively. But in conversational speech, I’m more frequently in the /chr/ and /jr/ camp!

