Here goes, a few things to keep in mind:
- Overflow hammers are only relevant on the first turn of a build. After the first turn they have effectively been added towards the build's hammer requirement, never to be heard from again.
- Conditional modifiers are just that, conditional. They don't come into play on every build.
- Permanent modifiers affect every build.
- The city advisor, as-is, displays base production + permanent modifiers.
- All 3 cities have forge/factory/power, giving them the dual 50% modifiers, these are permanent modifiers.
- The detailed production information in the city screen is accessed by mousing-over the hammers.
Domestic Advisor - Nothing special here, chopped out all the irrelevant info.
Nanjing - Turn 1 (not bothering to post turn 2, basically the same)
The basic production info, base + permanent modifiers, matches the advisor.
Beijing - Turn 1 (note the overflow, which is added to the 1st turn's production)
Aluminum is a conditional modifier for the SDI.
Beijing - Turn 2 (overflow is no longer exists)
The 95 to 81 production change is due to the 14 overflow having been added toward the SDI.
81 doesn't match the 54 production listed in the advisor, but the base 27 + dual 50% permanent modifers does.
Kassite - Turn 1
Large overflow, this significantly skews the city's production compared to the advisor.
Kassite has the Heroic Epic, a conditional modifier for military units.
Kassite - Turn 2 (overflow no longer exists)
Ignore the change from 24 to 23 base production, I accidentally clicked the upperleft tile off before taking the shot.
The base 24 + dual 50% permanent modifiers matches the advisor's listed production of 48.
A bit of overkill here, but hopefully it can help anyone confused by the production listed in a city and the production listed in the advisor.
Edited to add mouse-over info
