As you referred to, higher productivity pays for higher wages. A growing economy with rising productivity supports wage growth. It isn't contributing to inflation.
Right now wage growth is running at about 4% to 5%, and productivity growth is actually declining. To get inflation back to target, we'll need to see some overall moderation in wage growth for the economy as a whole. That doesn't mean wages can't grow faster in some sectors and slower in others. That will reflect demand conditions in those sectors. It will also reflect productivity growth in those sectors.
If we want to sustain higher wage growth over time, we need to improve our productivity growth in this country.