The billionaire won't notice it because it won't exist; the billionaire will be taxed way above mincome, because otherwise how are you going to pay for it?
That's exactly the purpose of basic income. If a billionaire businessman replaces all of his workers with robots, all of his income goes directly to him. The laid off employees are now competing for the few jobs that are available which have not yet been automated, and not all of them will be able to find another job because other businesses are automating away humans too. We need a way to redistribute wealth from the billionaires who make their money off the efficiency of automation to the people who would have previously worked for them.