I am having precisely the same problem. I just downloaded a huge number of tattoos from the exchange, and only 7 of them actually show up in CAS, and one of them is just a recolour of the default mermaid tattoo.
When I look at my sims launcher, I can see all these tattoos, but they are all labelled as "style", while some have a "style" entry and a "CAS Part" entry. Like so:
http://i224.photobucket.com/albums/dd160/Jangji/TS3%20Tattoo%20Glitch%201_zpsmnusrdpl.jpg
Additionally, only some have their own thumbnails. The rest seem to have copied the thumbnail of another of the tattoos.
In any case, some of the tattoos I have showing in my Game Launcher under Installed Content:
http://i224.photobucket.com/albums/dd160/Jangji/TS3%20Tattoo%20Glitch%202_zpsvxkxckhx.jpg
And my CAS sorted for custom content looks like this:
http://i224.photobucket.com/albums/dd160/Jangji/TS3%20Tattoo%20Glitch%203_zpsyyzq6xza.jpg
So the only ones showing up are
- the arm band, which is called "Llna" as a Style object and "tenshlak_tribal10" as a CAS Part object,
- the chinese love character, which is called "Zank" as a Style object and "tenshlak_chintattoolove" as a CAS Part object,
- the tribal dragon, which is called "lost dragon" as a Style object and "uutattoo celtic dragon 2" as a CAS Part object,
- the Fairy Tail symbol, which is called "Fairy Tail" as a Style object and "LGP Tattoo #030" as a CAS Part object,
- the Naruto ANBU symbol, which is called "naruto tattoo" as a Style object and "ANBU Tattoo" as a CAS Part object
- and the Deathly Hallows symbol, which is called "Deathly Hallows" as a Style object and "Deathly_Hallows_TattoobyAlleyLee" as a CAS Part object.
Interestingly, there is a CAS Part tattoo, the "Tattoo tribal wings 01", with a Style name "Tatouage", that doesn't show up in CAS.
Further note: I don't have Ambitions, but I made sure when I was taking tattoos from the Exchange that they were tattoos that didn't list Ambitions as a requirement. I did grab a few in the hope they might work anyway, but the Launcher won't even install them without Ambitions. So between the OP saying that nothing changed after getting Ambitions, and the fact that a few of them are working, I'm tempted to say that isn't the problem here.
What to doooooooo how can I have a perfect Derek Hale without his Triskele tattoo?! I actually found a Triskele tattoo on the Exchange, I was so excited, but it's not woooooorking!!