13% RH is not achievable in most humid climates. In fact, it was 103 degrees and 20% humidity where I live on Monday. A humidity below 50% is ideal, but I don't believe you will have mold or mildew problems at the 55% you have already achieved. Condensation would not likely occur. Using a dew point chart can help:
http://www.porterpaints.com/products/techbulletins/tb12.pdf
At 55% RH and a basement temperature of 70 degrees, the dew point is on 53 degrees F. So if walls are warmer than 53 degrees you will not have free moisture to cause mildew. For every 5% drop in humidity, the dew point will drop 3 degeees F. Note 13% RH is not even listed as it is generally outside the realm of naturally occuring moisture levels, even in the desert.