Definitely not. Russian has no aspirated consonants at all, nor would they pronounce them in the Latin alphabet. In fact a Russian would pronounce the roman "T"

Definitely not. Russian has no aspirated consonants at all, nor would they pronounce them in the Latin alphabet. In fact a Russian would pronounce the roman "T" exactly the same way a Mandarin speaker would pronounce the pinyin "D" so I don't think there's much credence to your instructor's story.