There’s nothing wrong with the secure delete built into AxCrypt. Where the problems may arise if it you’ve got a backup system on the network share which retains deleted files.
Even if you perform a secure delete then any backups, if held, would still be available unless you did a secure delete on them too.
The absence of any visible file means that AxCrypt has deleted the original file and the original file only.
Take note that modern hard drives like SSDs use wear levelling technologies which make secure deletion almost impossible – short of physical destruction: incineration, shredding, degaussing etc.