The thing you seem to be confusing is preflop and postflop play here. Preflop a bet/raise is considered in terms of bbs. As stated in cash a standard raise size is 4xbb + 1bb per limper preflop. However, postflop you shouldn't think of bets/raises in terms of bbs anymore. instead you should begin thinking of them in relation to the size of the current pot. On the flop in the KK hand the pot was $0.19c. Therefore, our hero put out a pot-sized bet (PSB). A standard amount to bet would be anywhere from 1/2 - full pot (50%-100% of the pot). Then the villian raised. It's a minraise because when someone bets you can't raise less than than 2x what they bet. That is to say if I bet $10 on a flop you have to raise to at least $20. So our hero bet $0.19c (PSB) and was raised to $0.40 or $0.21c more which is just a small $0.02c more than a minraise.

To go along with standard betting amounts a proper raise from the villian here would be somewhere along the lines of 3-4x the amount of the original bet of $0.19c, which is anywhere from $0.57c to $0.76c. But of course you don't have to raise the exact amounts.

So preflop we raise in terms of bbs. And postflop we raise in relation to the pot. So an example would be in a $1/$2 blind game. I open UTG to $8. It folds around to the BU and he calls and everyone else folds. The flop comes (pot of $19 due to my $8, BUs $8, SBs $1, and BBs $2), and I bet 2/3 pot, which is around $13 and he raises to $36 or so. Just a quick pointless example. Hope it helps a little though.