Considering that the predator is essentially imposing a form of mind control on its prey by forcing them to fail to see its presence, there is no reason that the predator cannot simply wipe all possible senses of the prey from detecting it (eg hearing, smell).
It is generally easier to shut down all independent volition entirely than to precisely target the sight of the animal. An example can be seen in the emerald cockroach wasp, which preys on cockroaches. The cockroach, once injected with the precision neurotoxin, is incapable of escaping or even moving independently, and has to be guided by the wasp into a burrow, where it will be devoured by the larvae of the wasp. In this case, the wasp only needs its prey to be alive, but not capable of independent action.
As already stated in the comments, it does not make sense that an animal with such an extreme degree of control over its prey would not be able to use the same abilities to directly target and kill/incapacitate its prey. Therefore, the only reason the predator is rendering itself invisible is that it needs its prey to be alive and conscious. Otherwise, there is no discernible evolutionary benefit to have such a form of mind control, when its mind control apparatus is powerful enough for direct killing or incapacitation.
Using mind control also solves the problem of the predators being unable to target conspecifics with their invisibility, as their mind control techniques cannot be used on species which also possess mind control.
An example comes to mind are the Thrintun from the Known Space series by Larry Niven.
The Thrintun evolved on a planet where most animal species possessed telepathic ability. Natural selection led to an environment wherein no individual species possessed great advantage over any other; defenseless off-world species, however, were easy prey. A single Thrint can manage a few dozen sentient beings simultaneously; with an amplifier helmet, the same Thrint can control an entire planet.
Thrintun referred to their telepathy as "The Power". In all their religions, The Power was self-evident of their manifest destiny to rule the galaxy. A loss or congenital lack of The Power is cause for exile, or more usually murder by the family, in their society. These unfortunates, called Ptavvs, are tattooed pink and are enslaved by other Thrintun.
Their success in spite of low intelligence and poor skill with tools was due to the great advantage of their telepathic abilities; they never suffered much selective pressure to improve what they had. A Thrint's slaves could be far more intelligent than their master, but intelligence provided no protection at all against enslavement.
In your case, the predators could be using their innate mind control capability to render themselves invisible to their prey, while at the same time enslaving their prey to do day-to-day tasks which the predators are themselves incapable of performing. The predators periodically cull the population of prey/slaves for food.