Most concepts I have seen applied to the basic income is that it isn't just for living off that wage rather a income you could supplement with other jobs to make a decent living wage. This means everyone in the country would receive it (not just those making under 'x' amount of money) and all income after the basic income is taxed.
For example many of the areas where it is unlikely for computers/automation to completely take over is the service industry. As mentioned you could reduce hours but if there is no financial incentive for individuals as why would they. We have this issue with the local steel plant, they could easily hire and train more trades people however some individuals would have to take a cut in hours and overtime (mainly overtime) which they don't want to do as they value the money more than others working.
Part of the solution to this cut is to add in the basic income which is guaranteed, which when supplemented by your part-time odd jobs becomes a decent liveable income.
The problem with this idea is our current system is based on the principle of you do work and you get rewarded. The problem is as technology advances the amount of work available decreases (think about how many jobs are public sector now over private sector, and compare that with historical numbers, the reality is we create jobs with our governments bureaucracy because otherwise we likely would have a revolt on hand due to lack of jobs). As seen with the Industrial revolution and the Luddites, it can destroy people (mass suicides amongst skilled craftsmen in the late 19th century, due to being put out of a job). This means we might have to re-envision what qualifies as work, and things that were once seen as hobbies (such as book writing, or hobby woodworking, or gardening) might be considered work.
If technology continues to advance at the rate it is going, I can see the need to re-envision how we view society. Capitalism might have to be completely rejected (realistically globally what we have isn't capitalism, it is actually much more of a monopoly system at the moment, capitalism actually being SMALL business competing against each over to drive down prices, well instead we have large business that buy up any competition and fix prices) and a new economic model adopted.
Personally I am much more in the modern luddite camp and saying we should reject most technology and revert back to a much more manual labour based system (mostly handmade/machined items, manual accounting, etc.) as I feel it provides the most satisfaction for the amount of work done (well still keeping people employed). To me things like sitting at a computer typing out forms all day is not satisfying and I would rather make something with my hands which I can personally take pride in and see than some electronic work that realistically is never truly done (such are the miracles of bureaucracy).
I hope my ramblings on this topic have maybe put a bit of a different light on it, I am not 100% sure what I was getting at with it other than we will likely need a lot of change in our viewpoints to adopt to the future world.