But tariffs don’t cause prices to go up all across the economy in general. Domestic products will get more expensive in the short term due to a positive demand discontinuity, but they will fall again in the medium term as domestic producers regain access to the large swaths of the market they lost access to under the old global free market trade policy. If the tariffs continue for a long time (not guaranteed) then domestic labor compensation will also recover (perhaps not fully due to automation, but automation on the high volume stuff would free up workers to work on smaller volume products).
Side question - would you consider the converse, globalization, to be a deflationary force?