I don't know if this is true, but it seems to me that the point of articulation of the tongue tip against the roof of the mouth for the alveolar tap varies depending on the kind of sound that precedes and follows the tap. If I were to say "ara", I find the tongue tip hitting my alveolar ridge. On the other hand, if I were to say "oro", it feels like the point of articulation is further back. Can't say if it is post-alveolar, but it is pretty close I think. Does such a variation change the sound and nature of the tap in general, or is the alveolar tap a sound that allows variation in general? Just want some insights and feedback on this thought of mine since I've been told that the alveolar flap always hits the alveolar ridge, not post-alveolar. Thank you!
When we say "the alveolar this" or "the velar that", we're seldom talking about a sound with absolutely only one possible articulation but a whole class of similar sounds whose differences are not considered relevant in whatever context it is. So what falls under "the alveolar tap" is dependent on context, e.g. the phonological system of the language under discussion.
Adjacent sounds are "coarticulated" in some way or another, with gestures that anticipate what comes next. /k/ in key is made further front in the mouth than in cough, and less so in come. In the beginning of quick or cool, it often accompanies lip rounding. But we call all these sounds a voiceless velar plosive because those differences are not distinctive in English.
In North American English, [ɾ], the intervocalic allophone of /t/ and /d/, indeed varies in articulation depending on phonetic context. Derrick & Gick (2011) devise four classifications: alveolar tap, down-flap, up-flap, and postalveolar tap (found in autumn, Berta, otter, and murder, respectively).