I'm wondering, is this the nature of hard clipping in digital amps, to begin before there is any real noticeable distortion or is something wrong with the amp?
Yes this is normal. SS amps generally clip all of a sudden and they can sound very bad when clipping. The main advantage of tubes is that they "soft clip" - a much more pleasant and often cherished sound. As a general rule you should try to ensure that SS amps do not clip with tubes it is a matter of taste - a bit of clipping can add significantly to their rich sound.