What you're hearing is the slight delay of the DSP's in the H9, caused by mixing together the dry signal through the MixingLink and the dry signal from the H9.
There are two ways to deal with this, essentially making either the H9 or the MixingLink your master mixer.
1) Set the MixingLink's "Mix" switch to FX Only. This will make the MixingLink's mix knob a just a level controller for the effects return. In this case, you would use your H9 for Dry/Wet mix.
2) Enable KILLDRY on your H9 (or set the mix to wet), and your MixingLink Mix switch to either Dry+FX or MIX (depending on what you prefer). In this case, only the wet signal will come back from the H9, and the Mix knob on the MixingLink will be your Dry/Wet mix.
In either case, you might want to look into experimenting with the H9's three bypass modes as well. Note the user manual at https://www.eventideaudio.com/products/stompboxes/multi-effect-processor/h9#block-views-downloads-block-1