Very good question!
Usually yes, we will manage the position on the timeframe from which it originated.
I say usually, because there will be occasions when we need to be flexible & drop down or scale up a timeframe to locate an appropriate technical level to hide stops or locate a stop order to compound a move.
Obviously, that flexible & discretionary type of activity is always dictated by the market. We don't subscribe to the usual rigid or inefficient methods of pre-determining risk-reward ratios. Markets simply don't operate that way
For instance: we might have executed an order on the 4 hour frame, but need to drop down to the 1 hour reference to slim down an appropriate technical zone to hide a stop. Same when going up the scale from say a 4 hour to the Daily in search of a level to guage a (forward) potential supply-demand zone.
It’s extremely rare however that we’ll wander too far from our template frame to manage a position.
Slightly different for intraday trading, but then that’s a whole other kettle of fish altogether.