OK, the rule is this…
Using the example: russia falling to Germany…
UK and USA can NOT use the Caucuses IC if Russia has forces in Caucuses OR even if UK and/or USA have forces there.
However, IF Germany takes Caucuses, and UK or USA liberates Caucuses, then the nation that liberated Caucuses from Germany DOES get to use the IC AND collect income from it… so long as Moscow is enemy controlled.
Once Moscow is liberated, any and all Russian territory that was liberated from Germany by US and UK forces immediately reverts to Russia control… no more builds, no more income.
The key points are that:
The capital must be enemy controlled
The territory (with or without IC) must be taken FROM the enemy in order for an ally to use it.
So… if Russia falls, the UK can;t just walk in to Russian held Caucuses from Persia and take control… even if there are NO Russia forces in Caucuses.