I pronounce "privatize" as "praiv^taiz" [corrected by editing] instead of "private eyes"(praiv^daiz) [corrected by editing] despite the t being in the unemphasized, second syllable and appearing in between two vowels, and "lantern" with the t plosion, despite an n being in front of the t and a vowel appearing afterward, like "center" which is aptly pronounced "cenner" in accordance with the rule.
The pronunciation rules that I looked up seemed to suggest that "private eyes" and "lan-ern" were the correct pronunciations. But this is not the case among English speakers (or at least that's how I suspect things to be, having attended English speaking schools for a decade).
Why is this "t" rule not applied consistently? Or is my pronunciation wrong? My pronunciation seems to be in line with the dictionary's standard one at least.