All one has to do to demonstrate this is with a bit of micro-surgery make an incision between clusters of cirri, severing any connections. But you can't do this with Paramecium and the vast majority of other ciliates that have orderly rows of identical cilia anchored in place. There the rhythm of adjacent cilia appears due to the retarding effect of the surrounding water upon the close crowding of one cilium to another. One cilium is stimulated by the preceding one after a delay calculated in milliseconds that is caused by the water's interference, and when this occurs in sequence down a line of thousands of cilia, waves of contraction are clearly visible. When you look at rows of beating cilia, it is easy to be reminded of Roman or Phoenician galleys, except those early ships were propelled by banks of oars beating in unison, usually synchronized by the sound of a drum or gong.
Animals using cilia do a better, smoother, and more complex, job.
The way I explained it to zoology students was to imagine a field of grain waving in the wind. From above, you see spaced, rhythmic waves parading across the wheat field, yet you know the plants aren't going anywhere. Alternating stiff bending and relaxed recovery of wheat stalks would result in undulating waves. It is a beautiful sight under a microscope to an observer who realizes this is an action originally derived from simple creatures that came to live together in the dawn of life. The benefits of this arrangement are not hard to imagine, for both partners would be aided by moving to new areas where food might be more plentiful and conditions more favorable.