The longbow’s base attack time is 1.62s (which I even tested to confirm. Indeed this is the actual time).
With Network of Castles (15% attack speed) the attack time should become 1.62/1.15~1.4087 say 1.4 . The tooltip shows 1.37 and it is not a visual bug, I actually measured 1.37s (e.g I got 186 attacks in 255 seconds, 255/186~1.371).
With the Network of Citadels upgrade (30% Attack speed), the longbow is supposed to have an attack time of 1.62/1.3 which is roughly 1.246. Indeed, I actually measured an attack speed super close to this number but the UI value shown is 1.29. This part is a tooltip bug
The following table summarizes the situation. Blue numbers are the ones with no problems while the red ones correspond to bugs.