?????????????????Not when their pay increases that rate of inflation.
If their pay is keeping pace with inflation, or driving the inflation then by definition, they aren't losing out to inflation.
The situation in question screws over risk-averse investors and people with savings in their mattresses/savings accounts.
When the minimum wage doesn't go up, but inflation does, the minimum wage worker has lost in that scenario. When the increases in the minimum wage are the primary driver of inflation, the minimum wage worker is keeping up with inflation.