Tim appears in flashback sequences as a random child who has gone to see the Flying Graysons the day Dick’s parents die. He sees Dick Grayson performing a quadruple somersault, and the ringmaster says that only three people in the world are capable of that particular move. When the Drakes are leaving the tent with the other audience members, Tim looks back to see Batman in the shadows. This is the start of his interest in Batman - he says that he has clipped every news article on the Dynamic Duo and followed their exploits enthusiastically. After Jason Todd’s death, Tim notices that Batman is becoming more brutal and careless. He thus takes it upon himself to intervene, and contacts Dick Grayson. He lays out how he managed to deduce their identities - I will look at the “detective” side in the next post - and explains to Dick that Batman needs a Robin. Unfortunately, Dick flatly refuses to take up the Robin identity again. Tim is devastated, as you can see in the last panel. From the reader’s perspective, this is really unsubtle: Tim sees Batman and Robin as larger than life, as heroes, as inspirations to people like him. He dreams about being Robin sometimes - to the point where he has worked extremely hard to increase his physical fitness and gets straight As. Even at this early stage, he is prepared a contingency for no Robin - to take the role himself. Not out of true desire to be a superhero, but because he is convinced it is necessary for someone to do it. The idea of there not being a Robin is inconceivable.
The iteration “Batman needs a Robin” runs throughout these two stories. Exactly why Tim (or by extension, the narrative itself) thinks that “Batman is becoming darker because he doesn’t have a Robin instead of insert other Bat ally here”, rather than “Batman is devastated by the loss of a partner and doesn’t want to endanger another young life” is never really made clear.