Here are some screenshots of how this bug looks on my end:

As you can see, the Tooltip shows the correct amount. The City Details themselves, however, show 4 Mana less. This would be correct, if the city had an Essence-value of 0. 

The Tooltip for the Resource Bar shows the correct amount of Mana granted per turn, but the value for the city is still wrong. As soon as the next turn begins, the value for the city will be corrected. If you then open the City Details, the Resource Bar will again show the wrong value for the city.

If you dispel Meditation from the city, this happens: 

A similar problems exist with Research:

I still need to build the Alchemy Lab, to see if the Material bonus has the same problem. The Unrest-reduction bonus, however, works definitely.

One last curiosity: The bonuses work as intended, if you build a Scrying Pool and/or the Oracle. In this case, the bonuses work as if the city had an Essence-value of 1 (or 2 if you have both buildings).

Here are the first two savegames: Alchemist, Temple of Essence.

Edit: Removed pics and savegames, because they are no longer needed.