When exactly do I stop my watch and press the button?

Under Article 102.16.3B:

• Stand directly over your lane at the finish so you can see a touch above, at or below the water surface.
• Stop the watch and push the button the instant any part of the swimmer's body touches the wall, not when the scoreboard shows a time, and not when the swimmer looks up.

Finish touches by stroke:

• Breaststroke and butterfly: two hands touch together.
• Backstroke: the swimmer touches while on the back.
• Freestyle: any part of the body.

Stop at the touch even if you think it's illegal. Judging legality is the turn judges' job, not yours.