The Tigers are obviously at a disadvantage because the NL won the All Star Game again (Justin Verlander had a lot to do with that) and homefield advantage along with it. How bad is it?
Since 1980, the team with home field advantage has won 24 of 31 World Series. Of the 7 teams with without home field advantage, only 2 (1981 Dodgers, 1992 Blue Jays) lost Game 1. The only other team on that list to need more than 5 games was the 2003 Marlins, and none of them won in 7 (the 1979 Pirates were the last team to win Game 7 on the road in the World Series, home teams are 9-0 since).
It used to be commonplace to win Game 7 on the road in the World Series (1955, 1956, 1957, 1958, 1962, 1965, 1967, 1968, 1971, 1972, 1975, 1979). In fact, between 1955 and 1979, teams winning Game 7 on the road outnumbered teams winning it at home by an astounding 12-3. The Tigers are no stranger to clinching on the road, they've done it each of the last 2 years in the ALDS (including in Yankee Stadium, where that has rarely been done).
It is so unremarkable that it happened 3 times this year alone (every series except the Yankees-Orioles), but it almost never happens in the LCS either (the 1985 Royals, 1991 Braves, 2003 Marlins, 2004 Red Sox and 2006 Cardinals are the only teams to do it since the LCS became a 7 game series in 1985 compared to 9 victorious home teams).
Maybe the Tigers are different and can buck the historical trend. Their starting pitching dominated the Yankees like it was the '63 World Series, so maybe they can still win the series if they lose Game 1 or go to a Game 7, but they will certainly be an anomaly if successful.