Republicans and some of the media are touting how Republican turnout is way up from 2012, while Democratic turnout is down from 2008. Those are the years each party had their last competitive primaries.
Republicans sure benefitted from an enthusiasm gap in 2010 and 2014. Is there one in 2016? Not necessarily. There's not always a correlation between higher primary turnout and general election turnout. Primary turnout is always lower, sometimes much lower. The subset is sometimes so small that the higher general election turnout can change. We also shouldn't assume that people who vote in a primary are definitely voting that party in the general election. Many primaries allow independent voters or voters to declare their party affiliation the day of the election. They might be attracted to one primary over the other, but not sold on the party.
One of the reasons GOP turnout is up and Democratic turnout is down may be Donald Trump. Trump attracts Democrats and others who don't usually vote in Republican primaries. If Trump is the nominee many of his supporters may vote Republican in the general election, as they'll want Trump to have more of his party in Congress. There may be traditional Republican voters who might not vote Trump in the general election, but if the Republican party can get them to vote they're still likely to vote for the Republican congressmen and senators they always have.