好きな人に告白したら、サインを貰いました。(This comes from a manga)
I get the gist of the sentence, in that it means something like "I confessed to the person I like, but I received his signature instead" or "Even though I confessed to the person I like, I received his signature instead". Any idea on how to interpret the use of 〜たら here? Because I don't think that's a conditional sentence.
～たら Can also be used as "when" which it seems like it would work here.
仕事についたら連絡して。
学校が終わったら、お願いします。
If/when in English are so clear cut and used to contracts situations, it's hard to wrap your head around them sometimes. For translation purposes, there are many times when it's either. One of my favorites which is very common is when someone may or may not join you later (usually not): 行けたらいく. I'll go when I can. I'll go if I can. Either works.
When the second half of a sentence using ~たら is in the past tense, it's always "when". In addition, サイン here is, I would think, more naturally translated as "autograph".
When I confessed to the guy I like, he gave me his autograph.
While in this case the action in the second half (receiving the autograph) happened upon the fulfilment of the condition in the first (confessing), it is also possible to use たら where the conditional part is the act that caused the speaker to find out about something.
家に帰ったら、彼がいなかった
When I returned home, he wasn't there.
"He" may have left some time before the speaker returned home, so the conditional part here didn't necessarily cause the person to leave or disappear. However the speaker returning home was the condition for them finding out that he wasn't there.
