I'm experiencing something similar. I'll add some system and version information for me
Edit: Sorry, I've seen that you have also included system and version information in the meantime...
Game version: v1.70-(206bee6) (2018-12-21 14:25)
HTML5 Yes/No: Yes
Game world: zz1
Browser/IOS/Android + version: Firefox Quantum 64.0 64-bit
Operating System: Windows 10
Screen resolution: 1366x768
Account name: Foufour
Humans or Elves: Elves
Reproducibility: 5/5
Current situation:
I have 3 armories (each level 7), but my training size is only 22. When I have the mouse over two of the three armories, no tooltip appears, only for the third one it appears normally. Clicking on any of the armories opens the armory window, displaying "Basic training size: 6 + Your armories (3): 16 -> Training size: 22". The same holds for the barracks when I hold the mouse over the portrait of a unit in the production loop. Apparently only those armories where a tooltip appears are considered "acitve" by the game and contribute to the training size, whereas the others are counted, but seem to have a training size of 0.
Expected situation:
I expect my training size to be 54. All armories should have tooltips. The text in the armory window should read "Basic training size: 6 + Your armories (3): 48 -> Training size: 54"
Reproduction Steps:
1. Open the barracks' training window.
2. Start the production of any unit
3. Hold the mouse over a portrait of a unit in the production loop.
4. Notice the training size is lower than expected.
5. Close the barracks window.
6. Have the mouse over one of the armories in the city.
7. Notice whether the tooltip appears or not.
8. Repeat steps 6-7 for all the armories in the city.
9. Click on any of the armories.
10. Notice that the displayed training size is the same as in the barracks, but lower than expected.