Pretty much any analog-digital-analog process (meaning any digital effect, not just ours) introduces a small delay, usually a few milliseconds. If do an analog mix of the output of such a process with the input, you will usually get a phasing effect (to be exact, a comb filter effect like that produced by an unswept flanger).
This does not usually occur with a delay-based (e.g. delay, reverb, pitch change) effect, since the above delay is usually tiny compared to the effect's delay. One normally avoids this problem by doing a digital wet/dry mix, where both the wet and dry signal are subject to the same delay. In most cases, you do not mix an undelayed effect, such as a compressor, with the dry signal.