There are so many variables, such as joist spacing, subfloor thickness and material, etc., that no one could say for sure the tub will fall through the floor.
Can you open the ceiling on the first floor below where the tub sits on the second floor? If yes, you can add more framing material to support the weight better. Is this person working in the local plumbing supply shop an actual plumber who worked on two story homes in your area, allowing them to have the knowledge of how your home is constructed? I believe not, or why is he working in a plumbing supply shop.