I recommend reading the manual for your camera.
Also, Canon created a webpage with links to various tutorials on shooting tips and how to prepare/care for your underwater housing. It's worth a look.
Canon's Underwater Mode is a shooting mode that tweaks the white balance to compensate for the loss of red color at depth. If you think about it, the Underwater Mode pre-set will only have a certain range of depths for which it will work OK. However, at depths shallower than the usable range, it's going to overshoot on the compensation, making the reds too "bright" (overexposed). At depths deeper than the usable range, it's going to undershoot. It's up to you whether or not you want to use Underwater Mode. I never use it personally. For still photography macro subjects, I use the internal flash or an external strobe with the white balance set to Auto. For still photography wide angle-style shots without an external strobe, I turn off the internal flash and simply do the white balancing in post-processing. Years ago for video clips, I always did Custom white balance (using some white duct tape or a wrist slate) for my depth just prior to recording. I felt compelled to do this because my video editing program of choice (iMovie) at the time didn't have any free, built-in tools for adjusting white balance. At some point in the last few years, iMovie acquired a convenient white balancing tool, so now I just hold up a wrist slate at the beginning of the clip and do my white balancing for video in post. Very convenient.
Yes, the SD1300IS has several different white balance pre-sets: Auto, Daylight, Cloudy, Tungsten, Fluorescent, Fluorescent H, and Custom. If you really wanted to, you could certainly employ a Custom white balance setting for a given depth. Unfortunately, you'd have to recalibrate the Custom white balance setting when the colors change, i.e., you change depth. Depending on your image editor of choice, it might just be easier to white balance your photos in post.