Standard American English does pronounce those two words the way the Cambridge dictionary says we do: fail + jər and mill + jən. Generally, American English drops more consonant sounds than British English and ends up "slurring" sounds together as a result. This is just one example of that: the "L" in the middle of a word is often pronounced more like a "half-L" with the finishing "tap" dropped off completely.
I hope my answer helps. 如果看不懂，请说。我也可以用中文帮你解释。