The feared inflation-scenario looks something like this (using the example amounts above):
Day one: People wake up on the first day of the legislation's effect. Those who had been making $15k a year working minimum wage at Walmart now make $27,500. A large number of these people quit, deciding to live on the basic income of $20,000, which, for them, is still a raise.
Day two: Businesses are faced with rising demand for goods now that lower-class people suddenly have a lot of extra money in their pockets. They also have fewer workers to meet demand, so they end up raising both wages (in order to convince the remaining workers to stay) and prices (to match demand and cover their increased labor costs).
Day three: Rising wages and prices continue. Inflation spirals.