The noise mechanic in the game is about informing you of the direction of the nearest alien. In the original x-com game, it was possible to miss an alien as you explored the map and then have to completely re-explore the map looking for it. The noice mechanic addresses this problem and keeps the action and tension rolling.
There is no noise mechanic that alerts enemy units. Enemy Alerting is sight only.
There are a number of ways you can detect enemies without alerting them. GhostArmor, Sniper throw toy, seeing over half cover while on a higher altitude and out of line of sight.
As you said, if you discover aliens on your turn, that's very risky. Aliens get a free half action to move to cover, and then a full turn before you get a full turn. If your last guy discovers an alien, you're in for trouble.
Here's what I do to manage the risk of discovering aliens on my turn:
- the first two units I move (let's call them scouts) are allowed to uncover new areas of the map with a half move.
- If the scouts uncover way too much danger, you can move them back to safety with the second half move. The aliens usually follow you when they have numbers.
- If there are units (such as snipers) where I would rather take a reaction shot against no cover, instead of a normal shot with cover, I put those units in overwatch before moving my scouts.
- If I don't uncover aliens with the scouts, the remaining forces may full move, half move and reload, or half move and overwatch as needed. The only restriction is that they are not allowed to reveal more map.
- Scouts must have enough ammo to fire at least twice (this turn and next turn) before revealing map. If they don't have enough ammo, half move toward safety/full cover and reload.
If you discover aliens on your turn with this approach, you'll still have 4 full actions and 2 half actions to deal with them.