@Darkwing Duck Here's a journal article on the effect. You should read it.
One stigmatized feature of Utah speech is the “dropped t” in words such as kitten and mountain. We investigated three possible phonetic correlates of “t-dropping” by recording participants from Utah and other Western states reading a document containing several instances of /t/ followed by a...
read.dukeupress.edu
From the abstract, emphasis added.
"We investigated three possible phonetic correlates of “
t-dropping” by recording participants from Utah and other Western states reading a document containing several instances of /t/ followed by a syllabic nasal. The first possible correlate, actual deletion of /t/, was uncommon but occurred slightly more often in the mouths of Utahns. The second possible correlate was realizing /t/ as a glottal stop, which was actually done more often by non-Utahns than Utahns (89% versus 81%, resp.). The third correlate,
releasing the glottal stop orally rather than nasally (e.g., [khiɁƏn] and [mawɁƏn] vs. [khiɁƏn̩] and [mawɁƏn̩]) is the most likely candidate for “t-dropping” since Utahns did this in 17% of the cases compared to less than 1% in non-Utahns."
*That's* the Utah thing. It's not done by all Utahns, but it's done way more often in Utah than anywhere else. You're talking about the second one, I think, but we're talking about the third one.