Dirt poor people being slightly less dirt poor and not having to worry about where their next meal is going to come from will not inflate basic goods that much.
We've seen this with higher minimum wages. The amount of inflation is much lower than than the wage increase, and poor people end up with more buying power.
A serious distinction is that increased minimum wages incur a burden on employers which they pass around to their customers and business partners. The increase of burden is directly proportional to the amount of work of an hourly employee. UBI does not come from an employer and is not tied to an effort. There is no direct market burden, but yet an increase of cash is available none the less.
It should also be noted that inflation is not immediately present following a cash stimulus. It takes time for inflation to set in as a response to market conditions and as such inflation is measured as an adjustable change over a given period of time. That said specific single time examples of UBI not adjusting inflation only demonstrates a faulty understanding of economics.
Money at the government level is not a zero-sum game, so thinking it's as simple as raising taxes is an oversimplification, and while unchecked printing of money is problematic leading to inflation, how the monetary base grows would need to be part of a well-considered implementation plan.
the theoretical reasons for not increasing minimum wage is not inflation. it's a decrease in employment.
empirically, however, things are sticky and so we have not observed concomitant decreases in employment with (small to moderate) increases in the minimum wage. my other guess (not sure if this is supported by the literature) this can also be because not only is the market sticky, but because workers were being paid a lower wage than their employer could have afforded.
We've seen this with higher minimum wages. The amount of inflation is much lower than than the wage increase, and poor people end up with more buying power.