Coming back to post solution incase anyone else ever runs into something similar.
It appears the root of my problem was Busybox mount utility.
What I did is add this line at the beginning of my mount script:
exec >/home/tux/udev.out 2>&1
this revealed the error message: "mount: mounting /dev/sdb1 on /mnt/backup failed: No such device"
I played around with mount (adding -t ntfs-3g, adding the drive to fstab and doing mount -a, etc) to no avail.
Finally I instead tried to mount the drive using ntfs-3g utility with
ntfs-3g /dev/sdb1 /mnt/backup
(I am using a symlink instead of sdb1, just for readability sake I type sdb1)
which works perfectly via udev. Strange that mount command worked from shell but not from udev, but ntfs-3g appears to work.
Thank you everyone who helped!