I assume that the dual license here is on the terms of "either, or", meaning either AGPLv3 or a commercial license applies.
If you download it yourself and use it locally on your PC, or share it with your colleagues who work for the same business entity, with or without modification, then you are not required to fulfill the obligations of the AGPLv3.
If you download it yourself and distribute it to the public or to other business entities, or include it in your software or product which is distributed to others (the general public or other business entities), with or without modification, then you are required to fulfill the obligations of the AGPLv3.
In the case that the nuget package is used for a web service, if you download it yourself and use the web service locally only on your PC, or make it available to your colleagues (who work for the same business entity) as a web service on the company intranet, with or without modification, then you are not required to fulfill the obligations of the AGPLv3.
In the case that the nuget package is used for a web service, if you download it yourself and make the web service available to the public or to other business entities, with or without modification, then you are required to fulfill the obligations of the AGPLv3.
The obligations of the AGPLv3 above is basically to make the complete source code, build scripts and documentation of the nuget package and any other software linked to it statically or dynamically (including software you develop with it), with attribution, to those who either receive the binaries of software, or access it as a web service through remote network interaction (as mentioned in section 13 of AGPLv3).
If you want to use the nuget package without having to fulfill the obligations of the AGPLv3 in the case where you are supposed to, the only remaining option (for you or your employer) is to buy a commercial license for it.