(I would include a Wikipedia image here, but Imgur can't seem to handle a simple link, so you'll have to click it)
The answer above showcases the bacterial flagellum, which is indeed a molecular motor capable of whirling a protein around outside the cell. Paramecia, humans, and other eukaryotes have a more sophisticated device, consisting of nine sets of microtubules around a central core, surrounded by an extension of the cell membrane. Motor proteins (dynein arms) on each microtubule push against the others. The concept is similar to muscle motion, but this structure is capable of bending in many different directions.
In humans, cilia can form the basis of rather remarkable structures, such as in the photoreceptor where a single enlarged cilium forms the "outer segment" of the cell - a large piece of the total cell, anchored by one small connection.
In your aliens, hundreds of cilia might link an "outer segment" and an "inner segment" of a cell, and be capable of moving the outer segment in a two-dimensional plane relative to the inner segment. Assuming many such cells are stacked in a large array, each moved a little further by the preceding (one more step proximal) level of the array. the small displacement at each step would be amplified, allowing them to move a large tentacle as far as it can bend, in many possible directions. The tentacle could be bent in different ways at any point along its length, much as can (at least conceptually) with an individual cilium.
Such a tentacle would have no visible "muscles", and there would be no specific way to control it muscle by muscle. Rather, a set of nerve-like signals, carried by more traditional nerves to each position along the tentacle, would have to pass through all the cells at that proximodistal level. The pair of signals would control the motion in each of two directions. This implies that each cell would need to be able to pass two different kinds of action potential at the same time, each having its own effect, without confusing them. Perhaps the cells could have an innate rhythm, being open to depolarization action potentials at one stage in the cycle and hyperpolarization action potentials at the other. The frequency and pattern of each type, relative only to itself, would determine how far the cilia bend in one of two perpendicular directions.
The circulation nourishing the cells could pass through the narrow spaces within each cell that are bridged by the hundreds of cilia. This might supply the energy source needed for contraction extracellularly, directly to the membrane of the cilium, from which the energy could be routed directly to the dynein just inside the membrane.