The kitchen sink and bathtub have separate drain lines, all of the waste pipes in your house's plumbing connect together ultimately, which helps explain why draining the sink causes water to come up the bathtub's drain. The problem may indicate a small or serious problem with the house's plumbing. All of the drains in your house connect directly to smaller drainpipes, which transport the waste water away from the plumbing fixture. These smaller drainpipes connect to larger drainpipes in the house, which will capture the drain water from several nearby plumbing fixtures at once. When a clog forms in this larger drainpipe, the waste water that flows down one drain cannot flow down the larger drainpipe, and so it travels up another smaller waste line and up through another plumbing fixture's drain. Your bathtub's drain sits lower than the sink's, meaning the backlogged water will reach the tub's drain sooner.