The answer to this interesting dilemma is based on an understanding of dive physiology. The phenomenon you describe is known as immersion diuresis and occurs whenever the body is emerged in water. Immersion, along with a water temperature that is colder than air, causes narrowing of the blood vessels in the extremities. This vasoconstriction occurs primarily in the skin and superficial tissues of the body as well as in the muscles of the arms and legs. The result: An increased volume of blood is sent to the central organs of the body such as the heart, lungs and large internal blood vessels.
The hormone that controls the production of urine by the kidneys is called antidiuretic hormone (ADH). It controls when and how much urine your kidneys make. The increased blood volume to the major vessels is interpreted by your body as a fluid overload. This overload causes ADH production to stop, which in turn allows the kidneys to immediately produce urine to lower the centrally circulating blood volume - the body's automatic response to preserve blood volume.
Once you exit the water, circulating blood volume returns to near normal - less the fluid taken to produce urine, which is quickly replaced as the body draws fluid from body tissues, such as muscles. Unfortunately, you probably will also leave the water with a full bladder.
Since we are all subject to the same phenomenon underwater, this is probably your normal response to immersion. If this situation causes problems like urinary tract infections, see your doctor. If your coffee is caffeinated, you may wish to switch to a decaffeinated brand, as caffeine is a known diuretic that also interferes with the production of ADH.