This is due to unfinished work. Some of the background modes always send shifted characters; others always send unshifted characters. The problem is documented in many places on HotkeyNet's website including the top of the list of unfinished features:

Known bugs and incomplete features.html

I recently started revising the background modes so they do this properly. I think SendWinS and SendWinSF are now handling this properly but only in the special test builds where the new work is getting introduced. You can download the latest test build (169-5) here:

Test build 169-5

If you decide to try the test build, please be aware that you may have to adjust a few things on the new Send Mode Settings panel. You may have to check a box there to turn on the new version of SendWinS .