That's not quite what he said. He said, "we should replace the ragbag of specific welfare programs with a single comprehensive program of income supplements in cash -- a negative income tax. It would provide an assured minimum to all persons in need, regardless of the reasons for their need."
Today we don't have truly massive displacement of the labor force due to automation, so presently it would be mostly those who are working who would pay for it, and it would mean progressively higher tax rates for us. But remember *everyone* gets it, and remember in his hypothetical scenario the costs of what we now call welfare have been eliminated. As you make more you begin giving progressively more of the UBI you get back. I'd probably be paying back more than what I got in UBI, but I pay a disproportionate cost of welfare as it is.
And if you're unemployed, you're free to take any old job you like, say an apprenticeship for what you'd really like to be doing - and it ADDS to your UBI stipend. It doesn't take away from it or disqualify you from it like welfare does now. Or do nothing, if you wanted to just subsist and be considered at the bottom rung forever. I really don't think most people would be content to just fuck off full-time forever.
The minimum wage would be eliminated, since society had already taken care of that. So employers could get labor more cheaply, especially for apprenticeship-type jobs.
As "robots" began creating greater frictional unemployment (refer to George Stigler's concepts) then society would have to find a way to recoup some of the extra productivity they provided in order to pay for the displaced labor -- and that's a tough question to answer. That displaced labor wouldn't be displaced forever, but it would take time for each displaced worker to find a new spot in a heterogenous labor market - i.e., learn that new skill.
Yes immigration would need to be controlled, mainly in that as an immigrant you don't get UBI until you are a citizen or have spent X-years here paying taxes. And if you want to come here illegally, fine, as long as you are willing to work for shit wages and never get any closer to getting a UBI.
The fantasy part is thinking that it will be at all easy to transition from the screwed up dis-incentivizing system we have how (welfare) to a UBI. The government is too in love with its job as Nanny to willingly accept something where bureaucrats aren't nearly as much in control.