Learn Finnish: Poistuessani huoneesta sammutan tuulettimen katkaisimesta. - When leaving the room, I turn off the fan from the switch.

Words ending in the instrument suffix -in use the stem -ime- before case endings. These words also undergo reverse consonant gradation, meaning the basic form is 'weak' (single t in tuuletin) and the inflected stem is 'strong' (double tt in tuulettimen). Because it is the total object of the action sammutan, it takes the genitive-looking accusative -n.

What verb is the instrument noun katkaisin derived from?

It comes from katkaista, which means to cut, snap, or break. A katkaisin is literally a 'breaker' (a switch that breaks the electrical circuit). Like other instrument nouns, it is formed by adding -in to the verb stem, and its inflected stem here becomes katkaisime-.

Why is katkaisimesta in the elative (-sta) case here?

In Finnish, when you use a physical switch or button to operate a device, you usually do it 'out of' that control. While English says you turn it off 'at', 'from', or 'using' the switch, Finnish prefers the elative case (-sta/-stä) to show the origin point of the control.

What is the grammar structure behind poistuessani, and how else could you say it?