My input would be the same or similar to Howard. Rear tool post or inverted cutter with lathe operating in the reverse direction is best for most hobby machines.
My lathe is a little larger than a mini lathe (it’s a Raglan) – but it is rather older than any chinese mini lathe. I have no (or minimum) parting problems with a simple HSS cutter mounted on the rear of my cross slide. All parting-off is left to the power feed to just get on with the job.
Obviously brass would be cut dry at fairly high speed with a very sharp cutter. One must expect a nib to be left on either the part or parent metal. How large that might be is obviously down to the material, size of the part and other factors. If the cutter is too high, the part will simply be ‘pushed-off’ when near to finishing the cut, or break away at possibly a smaller diameter, if dead on the ideal cutter position. Clearly, if the cutter is set too low, ideally the cut would not be completed! With the cross slide being forced down towards the lathe bed, the cutting forces must be at the most consistent possible for a lightweight machine.
When cutting through to a central hole, the cutter, whatever it might be, will break through at the thinnest point and grab (think here a perfect parting cut with a very slightly non concentric hole). Finishing, after parting off, should be expected.
Your nib size may well be down to insufficient experience as well, so don’t give up!
The last point is always to part off with the cutter protrusion at the minimum necessary. Any extra is just another unwanted variable, whatever is being parted off.