Not really getting the “Conditional form followed by Past form” structure

Hi,

I’m not sure to understand the structure of these sentences:

1) パソコンの画面を見続けていたら、目が痛くなった。

〜ていたら seems to imply that it hasn’t happened yet, while 〜なった seems to imply that it has already happened.

I would understand a past + future sentence, as in 仕事終わった時行く、or a conditional + future sentence, as is 仕事終わったら行く、but I don’t understand this conditional + past sentence.

I don’t understand why it’s like this, nor do I understand whether the sentence says “(my) eyes hurt because I have looked at the screen too much”, or “if I look at it too much, my eyes will hurt”.

2) テレビをつけると、ちょうど好きな歌手が歌うところもだった。

Kind of same question here, conditional “つけると” + past (x)ところもあった。

What am I missing?

Thank you very much.

PS : These sentences come from a textbook, so I assume they are correct.