This is the 17404th most frequent Turkish word.
üzerindeyken
"While on it" or "while over it."
Here, 'üzerindeyken' is used to indicate a state of being located on the bridge during the act of being careful.
Köprü üzerindeyken dikkatli olmalısın.
You should be careful while on the bridge.
In this sentence, 'üzerindeyken' contextualizes the state of being above something, associated with the clear visibility mentioned.
Gökyüzü şeffaf ve berraktı, uçak üzerindeyken her yer görünüyordu.
The sky was clear and transparent; when the plane was above, everything could be seen.
Here, 'üzerindeyken' implies the condition of being on top of the beach during the enjoyment of the sunny weather.