Morgan, your sandbed won't be a source fo calcium for your tank, nor is it for those other tanks. Limesand, or crushed coral, is well suited for the biological needs of a sandbed, so don't think you made a mistake. I use a mix of crushed coral and sand myself. However, lime sand is basically just crushed live rock, which is limestone. Obviously, your rock isn't a source for calcium, nor will your sandbed be.
Calcium will break down, even your rocks, but it takes a pH of something like 7.2 or lower. This is how a calcium reactor works, by lowering pH in a separate chamber to break down the crushed coral that's in there. As the lower pH water from the calcium reactor flows through the media, it picks up calcium and other elements, and begins to raise its pH back up because of the new elements. This brings the pH back closer to an acceptable level as the newly calcium saturated water enters back into your tank.