This term is used with insulators those have very high resistance like teflon if they are used with "AC" signal and can not be measured as "negative".
Tan delta is defined phase of "current" regarding the phase of "voltage" generally, this is not rule of thumb though.
If one states "negative tan delta" concerning an insulator, who means much more "capacitive effect" than "resistive effect" of that insulator when it is used with "AC" signals, no matter with "DC".
You could obtain a +ve tan delta if you measure the phase of "voltage" referenced to "current" and this would be the same your "-ve tan delta".
If we say alternatively, "negative tan delta" is a convention, not a math result.