How does seafloor spreading cause continents to drift?
Seafloor spreading adds material to oceanic plates, causing the oceanic plate to come into contact with other plates but not necessarily causing those affected plates to "drift".
The image below shows the Earth's plates.
Seafloor spreading creates new oceanic crust at a mid-ocean ridge. When this new material reaches the end of the plate and comes into contact with another plate, whether continental or not, a convergent or a transform boundary will occur. Depending on the boundary type, the two plates will move (one subducted below the other or the two crash along side each other), but the seafloor spreading does't really cause the continental plate to drift in either case.
Note, material created at the Pacific mid-ocean ridge moving towards the Eurasian Plate will actually encounter the Philippine Plate before it encounters the Eurasian continent. As the image details, continental plates don't automatically end right when the continent ends.
Here's another image that may make this idea clear:
The new material is created due to seafloor spreading at the mid-ocean ridge. On one side, the oceanic crust is subducted below the continental crust. On the other side, the two plates collide in a transform boundary, which is a horizontal type of movement. The latter is the closest we really come to continents drifting.