Kind of wierd, but my guess is that the supplies are being sent out and when it gets to units what is left over begins to flow back toward the supply center.
There is no need to guess, the mouse over has the "returned to stockpile" mentioned earlier.
Like I said, this doesn't apply to direct from source overland supply nearly as much as convoyed. The difference (I suspect) is precisely because the "supply pressure" is already constant when you are using a direct from source overland method; even a relatively "short" convoy like those the UK uses to supply it's forces in France or Egypt would likely not suffer enough lag (and/or other issues that could compound)
So if you are playing Germany vs. Russia or vis versa it would not be as manifest because you are employing a "non-pulse"/non-convoy direct-from-source-overland route.
The reason I believe the convoys are "pulse" is because their movement is tracked (for sub interception & if you have your actual ships escort) depending on how many arrive determines how much supply arrives vs. how much was sent.
I also suspect it is at this point (arrival at the far off depot) that the new demand is registered back at the source (i.e., "did that convoy satisfy the need at the depot?" yes - stop / no - send another convoy with supplies from source)...and it is this "pulse" that over distance contributes to lag, vs. the constant "pressure" of the pull from the single-overland-source.
However, what I was indicating before is that the GUI/sliders actually don't take this "pulse" into account since the "return to stockpile" offsets the additional demands that a far off depot could be requiring (and still not getting)...which is why I keep my supply slider set "above" the required slider, by watching the mouse-over supply and comparing that to what is happening from the far-off depot to the front line troops it supports.
In some ways if you personify the home supply in this situation it is somewhat humorous in that bureaucratic way -- this supply general is sitting in Tokyo (supplyAI) and his reports (the slider status) indicate that all is well (green)...however he keeps getting these annoying messages from his subordinate in Rangoon about needing more supplies. Inconceivable! The status reports read "green"! The system is balanced! In fact supplies from other Indian ports are even being shipped back as surplus and returned to the national stockpile! Thus the Tokyo supply general disregards this report from the Rangoon depot for additional supplies, because the system is "green"
Now the real problem is that the depot needed to be moved closer to the front, a future feature of HOI would hopefully include the ability to select the port of your far-off supply depot.
