I've gone through a lot of Warmoth necks over the last several years, probably about a dozen just for myself that have been drilled for Schaller mini-lockers. Needless to say, I'm a big fan. They
are tight. They're supposed to be. A loose tuner is a shock/vibration absorber, which is NFG for tone/sustain.
Generally, they will only press in to within about 1/8" - 1/16" of the tuner body being in contact with the headstock. At that point, I thread in the bushing from the other side and tighten it down with a T-handle nut driver, which pulls the tuner body up tight to the rear of the headstock. They're in there very tight at that point. Line 'em up nice, mark the anti-rotation holes, then knock the tuners back out to drill those screw holes.
The only time I've had trouble was a couple Strats back, I used a set of GHS'
Schaller look-alikes by Gotoh. On one of those, using the threaded bushing to pull the tuner up tight actually sheared the bushing in half. Since they're imports, there aren't spare parts available, so I had to buy another set of tuners.
Now I've got some spare parts <grin>
Guitar necks are always made out of the harder hardwoods, so the wood isn't really compressible with hand tools and tolerances can be held pretty close. So, tight might be ok if you're not used to it. But, if it really feels like something is going to break, you might just wrap some 220 grit sandpaper around a pencil or a bit of dowel and dig around in the tuner hole to open it up a couple thousandths. Also, it may be helpful to wax the tuner housing with some beeswax, paraffin, a candle or crayon so the housing isn't fighting friction so much.