From SoCal here. Cal checks against their own records, not NICS for ammo sales. My understanding is the the Instant check with NICS has a very specific legal basis and is not funded or equipped to add other capabilities and/or checks for state specific desires. I'm a little surprised that the new system apparently didn't collapse. The record for implementing this sort of thing has been poor. The last registration process was poorly thought out and required a lot of info that seemed un-required by law, was hard to work, delayed, overwhelmed, etc.
There had been rumors and an attempt to put in "emergency" regulations requiring RealID for firearms and ammunition purchases so I helped spike sales, just in case. Apparently the few adults in the room in Sacramento determined that that wasn't going to be required. And the DMV is still struggling with the RealID.
So, I didn't buy ammo right off the bat on 7/1. I purchased a 455 Scout just before the 1 July point, including the 10 day wait, delivery 6/29. I have recently purchased some .22 lr for the Scout, etc. (The existing requirements for handling, purchase, delivery, etc., for ammo is a whole different set of discussions.) Part of this is the way this particular store works, part is the legal fooling around.
They "pre-qualify" an ammo purchaser by asking if we have recently purchased a firearm in the state. The check is against firearms purchasers listings. If you have, they file an on-line check. If not, the prospective purchaser has a different set of hoops to jump through. I had, including the extremely recent Scout. They used my CDL, did some data entry, recorded some info, grabbed the ammo I wanted, made some copies, fussed around, waited a couple of minutes. I came back ok. They took the paper and the ammo to the check-out, I paid and left. Impact on me was standing around a while. they had the impact of fussing about with the paperwork and I think that takes longer than advertised. This was mid-week, mid-day so not a long line. I'm going to guess peak times will be far more problematic just doing the paper for more customers.
If a "new" buyer, there is a background check, Ca style akin to a firearms purchase so it takes a while and the result is valid for a set length of time. I believe if a purchase is made during that period, then the regular check can be made after that.
Or, one can buy a firearm and do the check, then buy ammo.