My handset has CyanogenMod-13 on it. So I try mostly to use the included File Manager (from Cyanogenmod). It's not as capable as something like, say, ES File Manager, but also doesn't seem to have the same amount of bloat, adware, and spyware that others do.

There's also a different, far less capable, File Manager that pops up in the notification bar when I insert the USB stick. Not sure where that comes from, but I use its menu to "eject" the stick when done.

Mostly, I've been using the stick with TWRP for full flash backups, and for installing system apps like SuperSu.

Cheers