usually when someone says 'My signature' it's meaning is 'my name'. but in this case the item is their signature. So this can mean that this is advertised as their best product or their most important one. It's kind of like a signature to them! it's kinda cheesy in my opinion ^^;

thx for the correction Peachey..

The phrase is "I'm addicted to X". "To addict" does not work in the way you used it.

my sign-nature, is like your name, or drawing on a paper