Way too complicated to answer briefly.
Arnie also was not involved. Gray Davis was in office when the legislation took effect. Arnie was the governor after 2003 and the special election to remove Gray Davis.
Arnie signed the .50 BMG ban and some other things into law.
Assault Weapon restrictions have a long history in CA, going back to the Roberti-Roos restrictions of 1989 that banned specific firearms by name, but had no feature list, so nearly the same firearms with a different name were legal.
The magazine capacity restrictions came in 2000 as did the feature restrictions similar to the federal level AWB, and required registration or they were a felony to own subjecting one to 10 years imprisonment.
There was some court decisions namely the Kasler and the Harrott v. County of Kings County decisions that changed things.
Kasler required a new window of registration be allowed for firearms banned. Harrot essentially said some definitions of what was banned were ambiguous.
That banning all AR and AK series for example is not very clear. They cannot just determine what is or is not an "AR" and it needs to be specifically banned by model name.
As a result they had to add specific new firearms to the list, and those not specifically listed were not banned.
There was lists of firearms banned by names as a result, in addition to the banned by features list even for those not on the lists.
However when they banned new firearms they had to open a small window to allow registration of the new banned firearm so it could be registered as an 'assault weapon'.
The gun community managed to turn this into a positive thing to get around the prior 2001 registration deadline to own registered assault weapons.
The trick:
'assault weapons' don't have to comply with the feature restrictions that outlaw semi automatic assault weapons as unregistered assault weapons (with a typically closed registry). As a result those people that purchased a gun that had nuetered features that complied, and had thier gun banned afterwards, could register it an then add all the features that would otherwise have been illegal. Like pistol grips and detachable magazines, flash suppressors, folding stocks, etc
So the thing to do for some people was to then figure out the next gun model they were going to add to the ban list, and rush out and buy it before it was added to the list. Then register it in the registration window and have a grandfathered assault weapon they could have whatever features they wanted on.
So they stopped adding firearms to the banned list to stop this form taking place and made it law in 2007.
As a result the banned by name lists generally refered to as the Kasler list and the Roberti-Ross list are fixed at the number of firearms banned by name which are always assault weapons (and so illegal if not already registered) even just a bare receiver. Then there is still the banned by feature list that turns any gun with certain features into an unlawful and illegal assault weapon.
People are able to purchase guns which are 'off list' and either don't normally have the banned features, or have been specifically modified or adapted for the CA market to comply. ARs without pistol grips for example, or various firearms with a mag release that cannot be pressed by a finger rendering them legally a fixed magazine to name a couple.
The primary confiscation that has taken place so far had to do with some SKS rifles with detachable magazines if I recall.
They were outlawed purchased as such. However those modified into such rifles by owners were declared legal for years.
Then they changed positions and said no those are in fact banned as well.
So those who tried to register them then had the government come round them up and reimburse them what they felt was a fair dollar amount.
While the clear implication was 'You are in illegal possession, are lucky we are not charging you, and we are in fact even paying you for the rifle, so don't resist or things will get very bad for you. We know you have such a rifle as you tried to register it.'