I take no credit for what follows, but as the info was new to me, I thought it might be to some other users as well.

The credit goes to TidBITS-TALK where this subject was discussed very recently. This is a quote from that site:

Quote: I found this in the book “Take Control of Backing up your Mac (3.1)” by Joe Kissell. This seems to explain why the indexing was happening even with your Time Machine disk on the Privacy list.

“Spotlight always maintains an index of your Time Machine disk so you can search in your backups. You may be tempted to prevent Spotlight from indexing that disk by adding it to the Privacy list in System Preferences > Spotlight, but don’t bother. It doesn’t work;

Spotlight keeps indexing your Time Machine disk even if it’s on the list. But this is nothing to worry about, because Spotlight searches don’t normally display matching items on your Time Machine disk except when you’re on the Time Machine screen.”
Excerpt From: Joe Kissell. “Take Control of Backing Up Your Mac (3.1).” iBooks. End Quote

And this further reply from an Admin:

"Yes, it is perfectly normal for it (Spotlight) to be indexing. There is no requirement for it (Time Machine) to be added to your Privacy list and nothing you can do to prevent it."

This was news to me - maybe to others too?