Hi, my Time Machine drive doesn't mount as a Time Machine drive

Hi, my Time Machine drive doesn't mount as a Time Machine drive but a regular yellow HDD. This still allows me to back up my Mac but the problem is that the "Backup" files that I see in the "Storage" section of the "About my Mac" keeps residing inside my Mac's SSD.

Normally what happens is this - when I back up my Mac, all the "Backup" files residing inside my Mac disappears after the Time Machine backs up my Mac. This can be seen in the "Storage" section → the "Backup" files are gone.

Now, what happens is that - when I back up my Mac, the "Backup" files get converted to "Others" files and occupies about 20gb of space! I think this happens because my Time Machine drive doesn't mount as the green Time Machine drive but as a regular yellow drive on my Mac. Can someone help?