Mongols have Military Academy upgrade which increases production speed of military units by 33%
(like tooltip says). But if you research this upgrade and then research Military Academy (Improved) then your production speed will increase by 66% (but should be +43%).
I tested it for Rams. Before this upgrade their default production speed is 30 seconds.
If I go for Military Academy then they get 22 seconds (which is correct, 30 sec/1.33=22.55sec).
But if I go for Military Academy (Improved) then production time become 18 seconds (which is not +33%+10%=+43% for production speed). It is +66% for production speed if we take 30 seconds by default time (30/18=1.667=166.7%)
On a side note you also misread the tooltip. There is no 43% anywhere. 33% increased speed indeed for normal tech which is equivalent to 25% reduced production time. The improved version is intended to give 35% production time reduction which is equivalent to 53.8% increased production speed not 43%. (The normal tech’s tooltip describes the buff as a production speed while the improved version talks about reduction of productio time)
Nevertheless the bug is indeed there and the way the improved tech is researched has an effect on the outcome and you can check the thread linked above for more details (including tooltip vs actual time)