A UBI doesn't work like a normal spending program, because it's cash. If you're at the median and to fund the $1000/person UBI you have to pay an additional $1000 in tax, you aren't paying $1000 more, you're net of zero. The above-median person who pays $1200 in tax isn't paying $1200, they're paying $200. The below-median person who pays $800 in tax isn't paying $800, they're
receiving $200.
This is also why a cut off saves you nothing. If the person at the 85th percentile would have been paying $2000 in tax and receiving a $1000 UBI, and you eliminate their UBI so that they only pay $1000 in tax, zero real difference has been made to anyone. A phase out only changes anything if the nominal tax reduction it allows goes to a different income level than the people subject to the phase out -- but if that's what you wanted, you could do it by just changing their respective tax rates to begin with. Which is a lot easier to reason about, so that you don't do dumb stuff like impose a 35% UBI phase out plus a 25% marginal tax rate (effectively a 60% marginal tax rate) on middle income people, while charging a lower tax rate to higher income people.
More to the point, the context here is using a carbon tax to fund the UBI, which makes the point succinctly. If the average person is paying $100/month in carbon tax, it funds a $100/person/month UBI. A carbon tax is quite regressive -- more even than sales tax -- but the UBI is at least as anti-regressive, so it cancels. The only difference it makes is to the people with a higher or lower than average carbon footprint, so it gives everyone the incentive to be on the below average side, which is exactly the purpose.