Higher oil prices may be partly passed through to core inflation at least for a time,
Models used to describe and predict inflation commonly distinguish between changes in food and energy prices - which enter into total inflation - and movements in the prices of other goods and services - that is, core inflation.
I wouldn't be surprised to see core PCE inflation actually fall a bit over the next two years
You are seeing some pass through of high energy and commodity prices, import prices, into core inflation.