Earlier quoted context omitted.
Yes, this is unconditional and on top of any other income you get.
I did not see this anywhere in the article and most models of basic income i know do not do this. They instead only fill you up until you got amount X of money.
By giving the basic income to everyone equally, everyone has an incentive to earn more money at every point on the wage spectrum. Higher earners will still pay higher marginal rates (likely everywhere else). But the situation of the highest marginal rates being experienced by the poor (which is common) is eliminated, as are the expenses of administering complex benefits and means-testing regimes.