You can use this code snippet in the script repository to resample a segmentation to higher resolution. This should not be done in a segment editor effect, but anytime after you created the segmentation node.
An alternative is to crop and resample the input volume before starting segmentation. This makes things a bit simpler, as the segmentation resolution will match the volume resolution. Cropping the image to the relevant region at the same time when you are resampling can help keeping memory usage at a level that your computer can still handle. For example, oversampling a volume by a factor of 2 will increase memory usage by 8x; oversampling by 4x will increase memory usage by 64x. So, if you don’t crop the input image to the minimum necessary size then the image that your computer could handle with 16GB RAM, after 4x oversampling may need 1TB RAM.