How would we have gotten these alerts in the past? Is there somewhere you need to search, or do you get it for every wallet you have?
Every wallet which supported this protocol message (which should be every single wallet out there) would have received it over the Bitcoin network. It was one of the protocol messages along with tx, block, inv, getdata, etc. This means that these alert messages were sent in the same exact way that a transaction or a block is sent to the network, as a flood. If the message was valid, it was relayed by a node to all of its peers. They were only considered valid if they were signed with a specific private key which is controlled by satoshi, theymos, and a lot of other people that not even a key holder knows everyone who holds that private key.