What kind of fungus - early blight, septoria? Changing soil isn't always helpful as neither one of these are systemic. Also, fungal spores can blow in with the winds, be carried in on rain droplets, etc. What is helpful is to mulch well to prevent soil splashback onto the plants, and also to clean up leaves below the first fruit set (other than that, I generally don't prune).

I also use Daconil as an effective preventive for fungal diseases. It works by coating the plant and limiting further attachment of fungal spores.

As far as the advice you received at the garden center re the neem oil, sounds like the guy at the nursery meant well. But neem really isn't that useful in treating/preventing foliar fungal diseases on tomato plants.

Once a leaf has fungus, it's toast. The damage is not going to reverse. Best to remove it from the plant, so that the fungal spores don't continue to multiply on that leaf and contaminate the rest of the plant.