I don't believe mirrors and caches affect this behaviour.
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.
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.