While trisets are intense, they’re also very safe. That’s because fatigue means you won’t be able to lift such heavy weights, and that puts less mechanical stress on your muscles and joints.
However, because you’ll be pushing your muscles to failure, you should choose exercises where you won’t get crushed by the weight if you cannot complete a rep. That means dumbbell bench presses are fine, while barbell bench presses should be used with caution. Use a spotter for safety whenever necessary.