The daily quests each have a cheese in the corner, saying how much cc it will give you. However, for maybe a couple years they haven't been giving me the correct amount, only 10 cc for each quest.

I have circled it in red in the below image:

Here you can see that while I was supposed to get 20 cc for completing the racing quest, I only got 10cc.

Most of the cheese gets sent directly into your cheese count in the shop, only a part of it is given to you as cheese coins

Hello, that's normal. Every quests will give you 10cc and the other ones will be sent in your shop, as Khajiitos said.
If a quest gives you 50 cheese, then you will have 10 consumable cheese and 40 in your shop.

Okay, it's true, but why does it happen like that? I was hoping to get CC so i could get more tickets in the event!

Hello, unfortunately it doesn't work automatically, the quests will give you 10 cc to invet and the others you have in the circle automatically to the shop

Giving base cheese rewards w/o inventory items is pointless, since there's 250 limit for inventory cheese. Only way to resolve it is removing or raising the cap.