For a cognitive process to occur, all the essential conditions must be present. According to the Commentaries, the essential conditions for each type of process are as follows:
(i) For an eye-door process:
(a) eye-sensitivity (cakkhuppasāda);
(b) visible object (rūpārammaṇa);
(c) light (āloka);
(d) attention (manasikāra).
pg 151IV. COMPENDIUM OF THE COGNITIVE PROCESS guide to 4
Question, how exactly does kamma vipāka interact with the above conditionality? What exact role does it play?
Kamma done in the past is a given for the vipaka-citta (in this case cakkhu-vinnana) to arise. And here venerable Bodhi is listing some of the conditions that are needed to support/condition cakkhu -vinnana.
So the object is visible object (rūpārammaṇa) and if this is an ugly sight it is the result of an unwholesome kamma done in the past and the opposite for a desirable sight.
Dear Citta
here is a quote from the Visuddhimagga which gives conditions from the Patthana.
"firstly the eye element is a condition in six ways –
namely, dissociation, prenascence, presence, non-disapearance,
support, and faculty for the eye-consciouness (cakkhu vinnana)
element. The visible object is a condition in four ways , namely,
prenascent, presence, non-disapearance, and object for the eye-
consciousness element…."visuddhimagga xv40