Just a point to note.
The original problem is partly a system limitation of Windows, but also bad design in NMM.
Basically, when you download a mod on the site, we tell your PC to open a web link starting with nxm:// instead of http:// (this is called a protocol). Windows can only associate on app with nxm:// at any one time. M3Tweaks would have set itself default when you launched it. NMM has no feedback if it's not default anymore.
Vortex, by contrast, will take over the nxm:// handling each time you start it (you can turn it off in settings). This ensures any mods you start downloads for will be directed correctly to Vortex. ME3T may inform you next time you run it that it isn't able to process the downloads until you set it back to default.
At some point in the future we might look at providing a means to split downloads to different managers based on the game, but ME3Tweaks is the first (and only) mod manager that supports a game that isn't also supported by Vortex so it's very low priority at the moment.