Aspiration is a separate phenomenon. English also has unaspirated plosives — they just mostly only occur in word-final positions, like the <t> in "pat", and they are not contrastive with their aspirated versions.
What I was talking about was how the Spanish /t/ has the tip of the tongue just a bit further forward, so that it touches the back of your teeth. English /t/ is, for most people, purely alveolar, so there's no teeth contact.
