No, you are not correct.
The registered assault weapons are okay (for now), you got that right.
What has changed with the new legislation is your pre-2000 magazines which hold more than ten rounds are about to become illegal.
That's right, even though prior legislation "grandfathered in" those magazines and allowed you to keep them and use them, the new legislation withdraws that allowance. You must now get rid of them.
<rant mode on>
This is a legislative treachery. It proves how fickle and deceptive our legislatures are and how important it was to create the Second Amendment to Constitutionally protect our gun rights. This new legislation is unconstitutional.
<rant mode off>
I bought a bunch of ten round magazines to use. I am also keeping my high capacity magazines for as long as the injunction is in place and hopefully thereafter. I am certain the magazine capacity restriction will be found to be unconstitutional and, therefore, void.
ETA - I am not a lawyer. This is not legal advice. No lawyers were injured in the preparation of this post.