I can't reproduce this in terms of seeing images I've already tagged. I can confirm the following in Firefox:

1. In firefox, while logged into Commons, go to https://commons.wikimedia.org/wiki/Special:SuggestedTags
2. Add tags to an image, publish, and confirm them
3. Take note of the image you see afterward
4. Click on "terms of use" below the images
5. Navigate back to SuggestedTags via the browser back button
6. You'll see the image that you saw after you published tags for the previous image.

Basically, in FF, when you go back to the page the app doesn't seem to reload, it's present in the state it was before and shows you the batch of images that was fetched previously. But, I never saw any images that I had previously confirmed tags for.

In T238173#5661531, @AnneT wrote:

Basically, in FF, when you go back to the page the app doesn't seem to reload, it's present in the state it was before and shows you the batch of images that was fetched previously. But, I never saw any images that I had previously confirmed tags for.

This is consistent with my testing as well. In FF, the page returns to its exact previous state, and in Chromium, the API is re-queried. In neither case do I see images for which I've already voted.