On Fallout Shelter I noticed that when caps are collected from raising SPECIAL stat it does not count as caps necessary to claim the kind of objective "Collect x caps"... As if it's not possible to count this caps to complete the objective...

That is one of the flaws. Sometims count sometimes not count, no regular rules.

e.g. Weapons and outfit from lunchbox count, power, water, CAPs etc not count.

The worst one is "Assign x dwellers to the right room", practically not possible in the early game. in the end game, I have to assign all of them to the "Wrong Room" to wait for the objective.