How does tariff increase inflation? The Wall Street Journal claims that:


  Some are concerned over the likelihood of the U.S. adopting trade
  tariffs on imports from China. This policy option would risk
  retaliatory measures and hurt U.S. exports, a blow to growth momentum,
  while making imports more expensive in the U.S., fueling inflation
  pressure. (emphasis added)


An academic article also says that the relationship is universally agreed upon by economists (gated link): 


  If there is one idea on which all orthodox economists concur, it is
  that tariffs raise prices, that protectionism, without exception, is
  inflationary. Professor Samuelson, for instance, argues that tariffs
  reduce labor productivity and enhance “the cost of living” (1976, p.
  694). In the words of Coughlin et al., “protectionist policies
  increase prices” (1991, p. 25). According to the 1992 Economic Report
  of the President, “Trade barriers not only raise the prices of
  imported goods to consumers but also the prices of domestically
  produced goods” (p. 196).


I understand that tariffs reduce labor productivity by disallowing countries to produce in accordance with their comparative advantage. However, how does this lead to inflation? Is it because a decrease in goods produced plus the amount of money kept the same leads to inflation?
Foreign produced goods will see price increases directly as a result of the tariff, which adds to the prices of these goods.  The full tariff may not be passed through, as these higher prices will reduce demand, changing the supply/demand balance

Domestically produced goods will usually see price increases indirectly as a result of the tariff, as demand for these domestically produced goods will increase as a result of the weaker competition from foreign produced goods, assuming an upward sloping supply curve

Your quotes translate these likely price effects from tariffs into "inflation pressure"