Drop your jaw moderately. Touch the tongue tip behind the bottom front teeth and lift the mid-front part slightly toward the roof.

Americans pronounce exclusivity as ehks-kloo-SIH-vuh-tee (/ˌɛkskluˈsɪvəɾi/). In "exclusivity", the "t" between vowels sounds like a quick "d" — the tongue briefly taps the ridge behind the upper teeth. This is called the Flap T, and it's why Americans sound more relaxed than the textbook. It comes out as EHKS·kloo·SIH·vuh·tee. Stress falls on the third syllable — keep everything else short and quick. You'll hear it in sentences like "The exclusivity clause is a critical point for our partnership".
Record yourself saying "exclusivity" and play it back. The mic stays on your device — nothing's uploaded.
5 syllables, 12 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Drop your jaw moderately. Touch the tongue tip behind the bottom front teeth and lift the mid-front part slightly toward the roof.

Raise the back of your tongue to touch the soft palate (velum). Stop the air, then release.

Place your tongue tip near the roof of your mouth behind your top teeth. Push air through the narrow gap. No voicing.

Raise the back of your tongue to touch the soft palate (velum). Stop the air, then release.

Place the tip of your tongue against the alveolar ridge just behind your top front teeth, the same contact point as /t/, /d/, and /n/. The difference is what happens to the air: for /l/, you let it flow continuously around the <em>sides</em> of the tongue (that's why /l/ is called a lateral). Turn your voice on the whole time. Lips stay relaxed, no rounding or flaring. For the Dark L variant at the end of a syllable, also pull the back of the tongue up and back toward the soft palate.

Round your lips into a tight circle. Let your tongue rest in the middle of your mouth, slightly raised.
The textbook way isn't wrong — it's just not how anyone actually says it.
In "exclusivity", the "t" between vowels sounds like a quick "d" — the tongue briefly taps the ridge behind the upper teeth. /t/ or /d/ becomes a quick tap [ɾ] — sounds like a soft D. The tongue briefly taps the ridge behind the upper teeth.
Stress falls on the third syllable, not the others. Stretch SIH — keep everything else short and quick.
Don't pronounce the third syllable too fully. The unstressed syllable reduces to a schwa — the lazy "uh" sound — in casual speech.