Hey so I tested this out on my private server, I modified the gather rate using Gather Manager. Everything seems to be working correctly with the Efficient perk - but there is something I need to explain.
Efficient is not intended to provide more resources in total - instead it just extracts more resources per hit from the node. If a node has 2000 stone to give, an Efficient pickaxe will still only get (more or less) 2000 stone from it. The benefit however is that an efficiency pick might do it in 6 hits, while a vanilla pick might do it in 10. I hope that clears it up.
A good way to check this is instead of comparing the yield of resources at the end, see how many resources you get per hit. A normal pick might give you 10 stone per hit, while an efficient III pick might give you 15 per hit (just random example numbers). But you will still only get 2000 stone out of it at the end, efficient is just faster.
The discrepancy between getting 2000 stone and 19xx stone is just how the nodes work, sometimes it rounds weird and you may get a little more or a little less.