⁵⁄₁₆" is the maximum tool capacity of the tool-post, and 8mm being slightly larger may be too much.
Although the discrepancy shows up most with parting-off, which is I think is by far the most difficult basic lathe operation, it's likely your other 8mm tools are too high as well.
The cutting point needs to be on or just below the centre of the lathe's spindle axis. Even slightly too high causes the tool to rub rather than cut; it may look as it it's OK, but not really – the tool will quickly go blunt.
I started lathe work assuming that cutters of the same size just plugged into the tool-post. Not so. Safer to read ⁵⁄₁₆" as UP TO ⁵⁄₁₆" and select smaller shanks, which are shimmed up to put the tool point at right height.
My lathe will accommodate 12mm tools, which I use for rough work. I actually prefer 10mm shanks most of the time, and have 6mm shanked tools for fine work. Hefty shanks bend less than small ones, which is good, but they take up more space, which is bad. Much depends on the type of work being done.
Parting off is notoriously difficult and I recommend learning ordinary turning and facing first to get a 'feel' for the machine. Parting off with a small lathe is fussy squared. Tool at correct height, bend and flex minimised by locking all unused slides and reducing overhang, careful lubrication and swarf removal, and above all a steady but not too fast feed rate. Parting off is easier on a big lathe with a hefty rear tool-post and power traverse. Hesitant owners of small manual lathes will have a torrid time, especially if the lathe isn't snug.
Don't be put off by early failures; one problem is parting is counter-intuitive in that the correct response to trouble is usually to go in harder rather than back-off. Except when the tool digs in!
Dave
Edited By SillyOldDuffer on 17/11/2020 10:32:24