Is been 25 years since I took Japanese in highschool but I'm relatively certain that our textbooks had ち romanized as tchi which from my recollection seems more accurate to its actual common pronunciation.
I have seen chi and ti, both of which when qwerty typed on standard windows or mac produce ち. I have never seen it as tchi.
つ is often seen as tu or tsu.
I have been in Japan for over a decade.
“tchi” is the Hepburn romanization of っち. (Knowing very little Japanese myself, the first example that comes to mind is たまごっち → tamagotchi.)
Perhaps only in the case where it's preceded by the small tsu? E.g. "一人ぼっち" -> "hitori bo[tsu]chi" -> "hitori botchi"? That's what Wikipedia says [1], although I think it's also common to (incorrectly?) use "bocchi" instead.
[1] https://en.wikipedia.org/wiki/Hepburn_romanization#Long_cons...