Hello Jean-Bernard and welcome
It is such a shame you have a problem with your neighbours cat, but you are so lucky to be able to enjoy the squirrels that come to feed.
It must be a natural defensive instinct of the squirrels which will save them from the cat and other dangers. They come and feed, so they are reasonably comfortable with the situation, perhaps over time they will begin to trust you a bit more - they can't possibly know your intentions are good!
You probably can't stop the cat or get rid of it, but try being nice to the neighbour and explain how you want to attract the squirrels but the cat is a problem, ask if they could possibly fit the cat with a couple of bells on the collar ( offer to buy the collar and bells), you can't stop the cat coming to your garden but at least alert the squirrels he is around. The best way is to try and make your neighbour as interested in the squirrels as you are.
I imagine the ones you saw in Vienna are so use to human attention and the treats they bring that they are almost tame, and probably reliant on that food.
Feeding birds is the same, I care for them everyday worry about their young change their diet through the year and as soon as I walk out side most flee, but a couple know I will give them a meal worm and will follow me around.
Enjoy your squirrels, as I say you are very lucky, do you have any photo's of them for the gallery?