Are you sure they are safe? They know your private key after generating your address - how can you be sure they will never use it?
They don't know your private key. You give them the public key, they give you an offset that you use to generate the private key. But they do not know the private key for the vanity address. (At least, that's how the vast majority of such sites work.)
Here's how it works:
1) You give them only a public key.
2) They give you an offset.
3) You combine the offset with your private key to get the private key for the vanity address.
4) If they had the private key to the vanity address, they could subtract the offset from it and have the private key corresponding to the public key you gave them in step 1. So if this scheme is insecure, then someone could get your private key from just your public key, which would mean ECDSA itself is insecure.
Why exactly would this one be less safe than others? Like Vod said I'm mainly worried about my private key disclosure. Do you know other websites that give out vanity addresses that are "safer" than this one?
Ones that use the method I described above are safer than those that just give you the private key to the vanity address.
