FWIW, I think ASIair grabs the comet's newest coordinates when you set up an Autorun or a Plan.
But that creates a problem since it moves so fast. Friday night I had ASIair set to run a Plan session from 1815 to 0200 and then switch to the comet. Except the first three frames had only stars, so I paused the Plan and started an New Autorun for the comet and it centered it as expected.
However, Because the comet moves so fast after 40 5-min subs the comet was almost out of frame because the system was tracking the stars not the comet. I knew that was the case, and CometAlign in PixInsight worked fine, but it sure would be nice if it would track the comet.