For actual Teletypes, which are electromechanical devices whose output is ink on paper, there were these ways to move the print position (there was no actual cursor):
Carriage return: mechanically move typehead to column 1.
Line feed: mechanically roll the paper
Any printing character: move one place to the right after printing
From memory, I don't think an ASR 33 could implement tab or backspace. Tab expansion would be done on the host machine. Backspace probably would not be done at all, though I suppose you could simulate it with return and a lot of spaces (but for what point?)
So, with the exception of tab, neither device nor computer would implement any extra movement operations: it was simply not possible.
Other control characters:
I think that's about it for the control-character repertoire.
There were no general cursor-movement sequences because the hardware could not do those things.
In case you also include other serial CRT devices, sometimes referred to as "glass teletypes", then the answer is often the same as for emulators: there's something in there, at least from the mid-1970s likely to be a simple microprocessor, interpreting the character stream and doing what the control sequences tell it to do.
But note that not all glass teletypes implemented 'direct cursor addressing' capabilities. Early/cheap terminals were functionally the same as actual teletypes.