Relooking at the stream, I think I understand why the Academy and Manufactury look like they have 'weird math'.
Both say
Provides: +2
Yield: 3
I think the "Provides".. is provided Whether or not you are working the tile (Biowell health, Node healing, Array Orbital boost, Dome hit points)
The "Yield" is the tile yield of the improvement (ie only when worked)
So if you have a manufactury, your city gets +2
If you are Working the Manufactury, your city gets +5 (plus what ever the base yield of the tile is)
Which means if you are Working a Terrascape tile, it provides 4 food, 4 hammers and 4 culture.
If you are Not working it, it provides 2 food, hammers, and culture
Which means a size 1 city could have massive production..as long as you had enough energy to support the improvements it wasn't working.