It is working as intended.
The way ALL missions work, when you complete the mission requirement, you can collect the mission reward. There are 2 different missions associated with the letter ‘L’ in two completely different ways.
When you level up your player level 1 time, you complete the first mission and receive the first reward. This reward, then completes the second mission and you receive the second reward. There’s a chain event here - leveling up ends up completing both missions.
When you buy the letter ‘L’ (or choose it from a choice box), you will complete the second mission requirements and get the second mission rewards. But you have NOT completed the requirements for the first mission and therefore do NOT get the rewards for the first mission.