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Pete, see if this helps...http://handycrowd.com/drilling-brass-the-easy-and-safe-way/Bill
Something not right there Zee the DRO should change almost straight away, slight delay possible going from one direction to the other is to be expected due to backlash.
Zee, I suspect you have some backlash in the quill and once the cutting starts it pulls the quill down by this amount. Shouldn't happen if the quill is locked so you may want to check that...maybe it isn't locking properly.
Out of interest if you lower the quill say 1/2" by the lever handle then tighten the central hub lock to engage the fine feed what happens to the fine feed knob is you then try to move the levers up and down? Does it move in and out from the front of the mill head? if so it needs adjusting.
Well at least you should be able to work to a better accuracy than +/- 1/8" now