Time-reversed ultrasonically encoded (TRUE) optical focusing in turbid media was previously implemented using both analog and digital phase conjugation. The digital approach, in addition to its large energy gain, can improve the focal intensity and resolution by iterative focusing. However, performing iterative focusing at each focal position can be time-consuming. Here, we show that by gradually moving the focal position, the TRUE focal intensity is improved, as in iterative focusing at a fixed position, and can be continuously scanned to image fluorescent targets in a shorter time. In addition, our setup is, to the best of our knowledge, the first demonstration of TRUE focusing using a digital phase conjugate mirror in a reflection mode, which is more suitable for practical applications.