As a machine builder, we purchase oversize key stock and always hand grind them to exact fits for the application, so from our standpoint, we don't care how the key is called out on the drawing. Were simply given the parts and make it work as needed for the application.
As the machinist, we care a little bit more. The Machinist hand book has charts that call out exact dimensions for milling straight female key slots on shafts. Most of the time the other part is broached so dimensions are not super critical if you have the correct shims/bushing for the particular broach. But if your slotting that keyway, then you'll need the charts.
As the engineer, we should care the most, but usually we don't. Here's where having a solid support group of machinists and builders helps. If you don't, then you'll have to call out exact dimensions WITH tolerances for the shaft slot, and part slot.
So to answer your question, "yes a 3mm key would theoretically sit half way inside both parts", but there is a little more to that. The machinery handbook is your bible.