Assuming that the ceiling is drywall, no gap larger than 3mm is permitted. The choices include the hole saw and then patching or cutting a precise hole initially. I prefer the precise hole and make a template from thin plywood for marking the holes.

A Rotozip with a piloted bit can be run around the outside of the box carefully to cut an opening.

Unless the box is installed proud of the joists by the drywall thickness and extender is needed.

I think he's talking about old work here. I do a pretty good job just tracing around the box with a pencil and using a rotozip (Ok, not a real rotozip but my cordless dewalt rotary tool) to cut the hole freehand.

Brickeyee, you have helped me many times. That suggested a technique but did not answer the essential question of clearance.

Again, if I use a hole saw, and there is 1/4" gap along the flats of the octagonal j box, is that 1/4" gap allowed?

I am installing new work through ceiling wallboard, 4" octagonal metal j-boxes and blocking sufficient for ceiling fans.

Let me add I am as ham-handed with a rotozip as a keyhole saw. The R-zip gets away from me and it also makes tremendous amounts of dust. I look like a clown in whiteface and the room looks like it was dusted for fingerprints.

If I must keep a very small gap I will wrestle with the Rotozip but a hole saw would zing through the 4 or 5 holes needed.

What is the objection to using a hand-powered drywall saw? A little work? Your clearance question was clearly answered. 3mm is about 1/8".

The other tool I've started to use of late is a Milwaukee hackzall. It's essentially a very small battery powered recip saw. Use it like you'd use one of those "steak knife" style drywall saws but with less effort.

The NEC is 3 mm, or 1/8 inch from the box to the surface material.

Anything larger needs to be filled.

It is relatively easy to cut accurately on new work in drywall, a little harder in old work, and harder in plaster (especially on wood or metal lathe).

One old work a rotary zip cutter works very well on drywall nad even plaster on gypsum lathe.
On wood lath it is often time for the keyhole saw used by hand.
Make sure you have extra blades. The plaster (especially the base coats with sand added) take the edges of saw blades very quickly.
If you get more than a single box form a blade you are doing well.

I routinely just snap off the tip of the blades and use the still sharp remainder for other work.

I have "Klein Tool 702 Compass Saw Handle, Magic-Slot" and buy blades in bulk.
It makes short work off hole cutting as long as you have spare blades.
I used to have a handle that used sawzall blades, but it 'disappeared' on a large job. It was very nice.
Sawzall when you needed it, easily available blades for a hand saw when needed also.

Easysand20 is excellent for filing the occasional oversize hole edges.
It can be mixed thick (about like peanut butter (smooth only) and then used to fill the oversize gaps (unless they are really bad).
After doing a room just mix up a small batch and fill all the gaps.
It does not shrink enough when mixed with minimal water to even need a second coat.

(I thought I had posted this, but I don't see it so ...)

Bus driver, I mis-read your post. Thank you - sometimes I need stuff pointed out.

Brickeye, thanks for the extra tips. The current surfaces are gypsum board, some with heavy texture. I have sawn through all types of gypsum surfaces and yep, plaster-and-wood-lath is the most unknown. I never know if the lath will catch on the teeth and pull out more plaster, or something even more amusing. I will get a bit of easysand20 for errors.