You finally stated your actual motivation to ask this question, namely that your German teacher had pronounced a German word with the same tr-slurry, turning tragen into /tʃra:gən/.
But languages, despite being related, have completely different ways of using sounds and wildly different expectations of which sounds and which sound differences are important or not. Even languages which are really close, such as German and Dutch do not share many pronounciation characteristics — or frankly, pronouncing a name like Geert the Dutch way would not be understood in German to include a G out of the blue.
English and German are even less related than Dutch and German, so you can expect any pronounciation nuace present in English to be not true for German.
- English t can be realised as many things, from a glottal stop (‘wha’?’) over a normal t and, as you said, a ch-sound up to sh (nation).
- Japanese t is turned into a weak ch when followed by i and into ts when followed by u.
- I’m not even going to touch on the topic of Swedish t’s, which I assume to be worse than English. (Although I’m not sure which letter of Stenstorp is considered to create the i-sound in there.)
- Finnish t is always t no matter which surroundings it has.
- German is nice, because a t is usually a t, the only exception I can think of now being Latin words having a suffix starting with -ti (Nation, Potential)
In general, if you’re learning a language and realise your teacher is doing something that they would do with the same sounds of their native language, assume that phenomenon not to apply to the target language until proven otherwise by native speakers!
How to learn the proper pronounciation /tr/:
Start by trying to learn the r. It’s wildly different from any of the many ways English pronounces r.
Attempt to say tr. You’ll notice that using one of the correct ways to pronounce the German r, there is hardly any motivation to slurry the tr together into tschr.