To answer your question directly, swelling is present immediately after surgery, and is gradually reabsorbed as time goes by. Final results are not seen until 6-12 months post-op, which is why many if not most surgeons ask our patients to wait that length of time before requesting (or us recommending) revisional surgery. As your swelling goes down, the skin softens and relaxes, and fine surface lines and wrinkles may reappear. These are appropriately dealt with via peels or laser resurfacing. Skin does not tighten as time goes by, but as swelling is absorbed, appearance does indeed improve.
But, if the degree of swelling was great, or the degree of skin elasticity and natural collagen content low, or the amount of skin removal and tightening suboptimal, or any combination of the three, you may begin to notice skin laxity and crepe sooner rather than later.
Since the neck is the lowest area of the face that was operated on, gravity tends to make this area most susceptible to the effects we are discussing. An elastic chin strap worn day and night for the first week helps to minimize the collection of blood, fluid, and excessive swelling in this sensitive area, and I have my facelift patients wear it at night for a second week. For the first 3 weeks I recommend NOT laying flat at all, for even a few minutes, to reduce swelling that naturally occurs when your face is at the same level as your heart. Put a sofa cushion beneath your mattress rather than trying to "sleep on 2 or 3 pillows" because each of us rolls and pushes pillows aside, allowing the face to swell. Avoiding nausea right after surgery (retching and emesis) helps avoid excessive swelling and bruising, and use of ice bags if your surgeon allows this, are all that patients can do to help themselves get the best result possible.
The rest is up to the surgeon (and what he or she had to work with in the first place)!