Installing Linux Mint / Ubuntu onto a second hard drive with dual boot, Grub installed to second drive

I took out the CD drive in my laptop and installed an SSD in its place, using a HDD caddy. Then I proceed to install Ubuntu on the second disk using default but it ended up installing Grub on first drive containing Windows. This is a deal breaker for me since don’t like to boot into Windows via Grub. I used Boot-repair to get did of Grub, by disconnecting the Linux SSD. . Then reinstalled Ubuntu after connecting the second SSD, but this time I chose “Something Else” and selecting the Grub installation location as the second SSD ( /dev/sdb ) as shown here.
. I created only two partitions, one is 32GB swap since I have 32GB RAM, and the rest as ext4 root (/) . Now I have Grub menu only if I boot from second disk, and I can choose Windows if I want. If I boot from first disk, I boot directly into windows.