If you read the biographical entries of French generals in Six`s two-volume work, you will often find entries recording that (e g Macdonald, page 138, Vol II) was awarded a `dotation of 60,000 francs pension p.a. from Naples`.
Same page, M later received a dotation of 20,000 francs p.a. from Galicie`.
You will also often find such gifts and pensions awarded to French generals from the state of Westphalia: Vol I, page 148: General Boussart received in 1807 a dotation of 10,000 francs p.a. from Westphalia; in 1811 he received another pension of 4,000 francs p.a. from Hanover.
The examples go on and on. I doubt that these states volunteered these sums to French generals out of sheer gratitude.
N reserved large portions of the incomes of several vassal states for him to disburse as he wished.
You state that post 1810, cash flowed from France into the ex-Dutch army and navy. But from 1810 there was no Dutch army, no Dutch navy; they were French. The taxes raised by the French imperial treasury from the old Dutch provinces presumably flowed into the imperial coffers.
Being a state with a long coastline, off which the RN and hordes of smugglers hovered, the defence costs of such an area were liable to be high, thus the possibly negative cash balance between different parts of N`s empire - but it was all domestic French expenditure.