Behavior is very similar to Why do I have to hit tab twice to Alt+Tab away from Microsoft Excel? it is just related to SuperPuTTY.
I need to hit alt+tab+tab to switch to other application. Even if I have multiple tabs opened, there is just one PuTTY in task bar.
You will find why in this issue comments: https://github.com/jimradford/superputty/issues/216
It seems that Windows sees both SuperPUTTY and the Putty inside it as two separate applications: the first alt+tab moves you from Putty to SuperPUTTY, the second tab from SuperPUTTY to the next application.
