Whether to translate it as “when” or “if” is due to a distinction English makes and has little to do with Japanese.
たら focuses on a state where some event has just completed. If that event is hypothetical, “if” would be more appropriate. In your case, the main clause talks about something the speaker actually found out at some point in the past. Then the completed event of her waking up cannot be hypothetical.
The ～たら ending does indeed also serve as "when", not just "if". One of my Japanese teachers years ago explained this as a contraction from ～てから. While that fits for the meaning, my research over the years into Japanese etymologies suggests that this isn't the derivation.
The ～と conditional could sometimes also be translated as "when".
I expect you'll have a hangover when you wake up.
The ～えば conditional does not have any such "when" connotations.