Federalism can still work effectively in such a world because networking does not mean that people outside a given region can have political power in that region.
It is true that networking means that regions are tied together much more closely than before. California, for example, has more ties to other states than it once did and so things that happen in other states affect California and vice versa. This reduces the extent to which regions can truly be autonomous in a federal system.
At the same time, however, Californians can remain in political control of their own state. Actions taken by others may influence them economically, but it is still only Californians who get to vote for their own officials.
It is harder for regions to be autonomous in a more networked world, but federalism is still possible because outsiders cannot directly participate in the politics of a given region in a federal system.