Skill values are not integers (atrocious, pitiful, awful, etc. is just a different name for one, two, three), but rather include a fractional component that is not displayed. Someone who is inept.99 is almost mediocre.00 and will perform better in games, even though he will still be "inept" when you look at your roster. When a player trains, his skill increases, and occasionally the integer part increases and the "pop" will be visible and indicated with a green arrow.
DMI is calculated from the actual skill values, so should increase due to skill increases. But DMI also includes "game shape" which is much more volatile than skill increases. If a player doesn't play much in a week, his game shape will decline and so will his DMI, even his other skills might have increased.