When the GM announces, "you hear rumors of a new force in the east, gather power, seeking to eliminate all mankind", the GM is the Initiator. At that point, the Consequences will occur unless the PCs jump on the plot wagon.
Thats where Consequences runs the risk of railroading, being a prod to force player down a path.
As long as the PC can ignore the threat and do something else (consequences or no) it's not railroading. As long as the players have a meaningful choice, again, it's not railroading. If, no matter what the players seemingly choose, they end up confronting the big bad threat (even if they deliberately go in the opposite direction for example) then it's quite likely railroading.
Let's say at 1st level the players hear whisperings of a mad hermit working on a world destroying device, they ignore it and end the city's goblin menace instead.
At 4th level, they hear stronger rumors of a mad hermit gathering items for a world destroying device. As they've also heard of at least 3 adventuring groups and a city militia seeking out the hermit, they ignore it figuring they have easier and better things to do.
At 10th level, it's more than a rumor - the mad hermit has established a trap infested cave where so far no one has returned from. Constructs, undead etc. are known to guard the place. The king has put out an open (pleading) call for adventurers to help (as well as devoting his own army and resources) and many have responded. The PCs, having other obligations, politely decline.
At 15th level, while the PCs are in the middle of their current adventure - the world blows up.
The above may be a bit heavy handed, but is not railroading (unless you expand the definition so broadly as to make it lose all meaning).