A practical problem with these phased updates is that you may end up with different versions of some software on your fleet of (until now) identical servers and you have no way of avoiding it.
.. a job they should have left to the sysadmins in charge of those machines receiving said updates.
If the OS developers have the ability to save thousands of man hours of their users they should do so.
How this works is that the package index contains a stanza Phased-Update-Percentage: giving a number between 0 and 100. Then your client picks a number in the same range, and accepts an update if the repository's value is higher than the client's value.
Whether the fixed value comes from your mirror or Ubuntu's, makes no odds - You still have a fixed value on the server and a variable value on the client, so the outcome is still variable. Caching the index, or mirroring it without regenerating it, still leaves this decision to the end client.
Something else I found interesting looking into this mechanism - the seed for the rng is sourcePackage-version-machineID. So you won't "that one machine that always updates last" or "that one machine that charges head-first into phased updates", it should be randomly distributed for each version of each package.