How to use (으)ㄹ 때, do we need the past tense?

Hello, I have a question that arose while studying Korean. I was watching 'Steel Shining' on Netflix and got confused about how to use -(으)ㄹ 때. I especially don't understand the part where the past tense is omitted. The lines in question are from episode 2, around 37 minutes and 15 seconds: 'When I was young, my mom worked here for a while' and around 37 minutes and 47 seconds: 'When I was in Seoul for a short time, there was a guy named Hyungseok, his father had a study room...' Both of these sentences seem to be clearly talking about completed past situations, so I'm curious why the past tense is not added. Could you please advise on how to understand this part? I would appreciate any help in better understanding Korean grammar.