This seems to be a classical unix rights problem. Let's have a look on it. To avoid confusion I set user of /media/NAS to root and then check where is the problem:
pi@raspberry ~$ sudo chown root /media/NAS
pi@raspberry ~$ mkdir /media/NAS/folder-pi # works
pi@raspberry ~$ su -l pi2 # login as pi2
pi2@raspberry ~$ mkdir /media/NAS/folder-pi2 # works
pi2@raspberry ~$ mkdir /media/NAS/folder-pi/folder-pi2
mkdir: cannot create directory ‘/media/NAS/folder-pi/folder-pi2’: Permission denied
pi2@raspberrypi:~ $ ls -la /media/NAS/
total 16
drwxrwx--x 4 root nasusers 4096 Mar 29 10:13 .
drwxr-xr-x 3 root root 4096 Mar 29 08:38 ..
drwxr-xr-x 2 pi pi 4096 Mar 29 10:12 folder-pi
drwxr-xr-x 2 pi2 pi2 4096 Mar 29 10:13 folder-pi2
pi2@raspberrypi:~ $
Here we can see what has happend. Both users are in group nasusers so each can create folders in /media/NAS/. But the created folders get the user and group rights from the user, so pi2 cannot access folder from pi. /media/NAS/folder-pi is not in group nasusers. Also the group rights on the new folders are only read and execute r-x. We have to make sure that the group is inherited from the parent folder. For this we have the sticky bit. Also we have to make that the group gets rwx rights by default. For this is the umask. For it`s meaning look at the internet. Lets do it:
pi2@raspberry ~$ rmdir /media/NAS/folder-pi2
pi2@raspberry ~$ logout
pi@raspberry ~$ rmdir /media/NAS/folder-pi
pi@raspberry ~$ sudo chmod g+s /media/NAS/ # set sticky bit
pi@raspberry ~$ ls -ld /media/NAS/ # it`s set on the group
drwxrws--x 2 root nasusers 4096 Mar 29 10:40 /media/NAS/
pi@raspberry ~$ umask 002 # set umask and check
pi@raspberry ~$ mkdir /media/NAS/folder-pi
pi@raspberry ~$ echo "hello world" >/media/NAS/folder-pi/file.pi
pi@raspberry ~$ su -l pi2
pi2@raspberry ~$ mkdir /media/NAS/folder-pi/folder-pi2
pi2@raspberry ~$ cat /media/NAS/folder-pi/file.pi
hello world
pi2@raspberry ~$ ls -la /media/NAS/folder-pi/
total 16
drwxrwsr-x 3 pi nasusers 4096 Mar 29 10:59 .
drwxrws--x 3 root nasusers 4096 Mar 29 10:58 ..
-rw-rw-r-- 1 pi nasusers 12 Mar 29 10:59 file.pi
drwxrwsr-x 2 pi2 nasusers 4096 Mar 29 10:59 folder-pi2
pi2@raspberrypi:~ $
Now it's everything as it should be. For persistent settings of the umask you will find some information in ~/.profile:
# the default umask is set in /etc/profile; for setting the umask
# for ssh logins, install and configure the libpam-umask package.
# umask 022
Setting the default umask has a little disadvantage. It`s global and works also on the filesystem of your pi, so you have a little look at your group rights there.
And yes, as @Milliways answers you should use /mnt/ instead of /media/.