I have a Macbook Air that has 2 partitions on the hard drive. One is for Yosemite (450GB) and the other already has Mojave (50GB) on it.

When upgrading the Mojave to Catalina, I wanted to back up the Mojave partition and upgrade it.

But when I plugged in an external hard drive, Time Machine started to back up hard drive 1 first (450GB). Since I already set and boot up using Mojave, I restarted the machine, and ejected the 450GB hard drive, but when Time Machine started again, it still was backing up some 410GB of data, which means hard drive 1 is included.

So I went to Time Machine's Preferences, and clicked on Options, "+", and chose what to exclude: Hard Drive 1.

Next I rebooted the Macbook Air and wait for the back up to start, and it again, reported backing up 410GB of data.

How can Hard Drive 1 be excluded?