Make that ‘t’ sound again. Now, instead of placing your tongue wherever you do for ‘t’, place it on your upper lip, but otherwise make the same sound. It should sound somewhat like a ‘p’. What you have changed here is the place of articulation.
Place of articulation is made up in of two factors: the active articulator and the passive articulator. The former are categorically distinguished, as opposed to being a continuum, and consist of the bottom lip, the tip/front of the tongue, the middle/back of the tongue, root of the tongue/epiglottis, and larynx. The passive articulator is much more of a continuum, and includes the upper lip, as well as the entire upper jaw, from the teeth to the uvula. Some of the common spots include the, the alveolar ridge (T and D) and the velum (k and g)
Yet again, there is plenty of ground for speculation. If your speakers are a race with a large snout, perhaps more passive articulators on the now elongated jaw are due. A species with more distinctive tongue control may have 5 active articulation spots on the tongue, rather than the 3 that humans have.