The current practice is to specify the FINISHED hole size on your drawings (footprints, Gerbers, drill files, etc). A vendor who asks you for the drill size before plating is 20 years (or more) behind the times. I discussed this in old posts at, e.g., " Drill Hole Sizes " and " PCB Designing for 6 Layer ".
When specifying a hole pattern for press-fit, remember that there are several tolerance factors at work. Of course there is the tolerance on the hole diameter itself. For quick-turn, prototype, and short-run boards this reflects not only a basic, fundamental, machining tolerance but also a tolerance based on how your requested hole size (e.g., 0.0625") gets mapped into the sizes available from the vendor’s “standard tool rack” (where the closest sizes may be 0.060" and 0.067"). And there is also a tolerance on the position of the hole center. The most comprehensive document dealing with these factors is SEEED Studio’s " PCB Design for Manufacturing " manual (paper copy at " SEEED Design Guidlines ").
As others have said, you need to contact the PCB fabricator if your tolerance requirements are tighter than the vendor’s published values.
Dale