I would say it depends. 12.10.1.a says that there should be a incident response plan, and that it should contain at a minimum contain Communication strategies in the event of a compromise.
They dont say you need "at minimum to tell the payments brands", they say you need as minimum to "tell someone", you cant simply have a incident response plan that basically consist of "tidying up" and "securing the compromise" without notifying anyone.
If you decide to communicate to the indivual or to the aquirer, depends on the scale of the compromise.
Lets say a untrustworthy cash clerk photographs a single card in the POS with a camera while handling it for a customer and this go on unnoticed by the customer.
Lets say this are brougt out to attention.
Then its a lot whole easier, to just notify that affected indivual by phone, and ask him to suspend his card and order a new card from his issuer, than to notify VISA/MasterCard/aquirer of that small compromise.
It can be a good deal to notify the aquirer and say that the customer has been notified anyways. This will keep you off the loop in case the customer plays dumb and says he hasn't got any notification and decide not to suspend the compromised card.
If however, a CC database or whatever leaks out, or a website is hacked and replaced with a phishing site, its a really basically a must to notify the aquirer, since, hundreds, tousands or millions of customers might be affected.
The intention of 12.10.1.a is that all affected indivuals should get information about what happened. If you decide to itself inform all your customers, or if you go through your aquirer, is up to you. In most cases, its easier to inform your aquirer.