Hello again and thanks for clarifying. It seems—from what you write and from my testing—that the problem is purely to do with command-clicking on an image. I can confirm that the simulated command-click does not open the Web page in the background (when using Safari or another browser that is capable of doing so).
I do not know why the simulated ⌘-click is not working as expected, but I have a solution. I found a post by @noisneil which solved a different but somewhat similar problem, and I tweaked his macro to come up with the following one. Please confirm that it works for you too; else we can look at the issue again.
Mailmate command-click.kmmacros (23.1 KB)