19 minutes is plenty of time for a one-platform change, but this is good advice for any change.
A train is not like an aircraft; you don't have to remain seated until the train stops at the platform. In fact if you do wait, in order to get off, you'll have to fight in the aisle with passenger coming on at the station and you'll be like a salmon swimming upstream.
Pay attention to the time and the schedule and listen for the announcements. When you know you are coming into the station, get up, gather your belongings, and proceed to the door. When the train stops, the boarding passengers will let you get off before getting on.
Once you get off, locate the nearest stairs and proceed to them. They won't be difficult to find; most everyone who got off will be going there too. It will help if you already know the platform number for your connecting train, but you might want to check the departure board on the platform just to make sure. In 30 weeks of European train travel in the last 40 years, only once did a train depart from a different platform than the scheduled one. My travel was in Germany; I imagine the Swiss are at least as good at keeping to the schedule. The Italians - I wouldn't be so sure. I understand that the Italians never know at what time the train is going to arrive or what platform will be available when it does, so they just wait and see.
As long as you get to the platform with everyone else, others will be boarding, and the conductor is not going to release the train until everyone on the platform has boarded. Just don't dally, stay with the herd.