Gifting some cats in Antium should at least make sure that something at all gets moving.
A city attack unit should move towards Cuzco if it's his target city. But that should be true for all his other attack city units and I haven't seen a trace of them
. For the attack it will then calculate odds, so then we need very weak defenders.
It would be different for attack units, which can decide to attack from 4 turns away based on odds.
As usual there is the RNG involved in promotions. But attack city units prefer city raider (for cats also barrage and accuracy). Attack units prefer combat and unitclass specific stuff. A healer will be a counter, city defense, city counter or city special unit. Counter units also like terrain defense stuff. But also unitclass modifiers, so can look like attack.
If you see a crossbow with extra first strikes it will probably be a UNITAI_RESERVE unit (or counter with lower probability). That's an interesting unit as they will go for cities from some distance like attack units, if the odds are right.