but they don't think everything else will just inflate along with it?
The increase in wages is expected to greatly outpace any increase in costs for the poor. Even if everyone gets an equivalent pay raise, that only increases labor costs, not material costs. Gas won't go up 50%, food won't go up 50%, etc.
In fact the only thing that would go up by 50% would be labor-intensive services. However since the poor primarily spend their wages on goods and not services, they are among the least impacted by an increase in labor costs.