It doesn't happen here. When I tap on the icon, after I clicked on the home button while Activity2 was in the foreground, I'm taken back to Activity2.
B4XPages will solve all of this and will also make the navigation UX better as it will show the useful "up" indicator.
I guess that on your device the second tap starts the same app and treats it as a new task. Later when the second activity, which was already in the stack, is started, it doesn't behave as expected.
The logs look like this:
** Activity (main) Pause, UserClosed = true **
*** Service (starter) Create ***
** Service (starter) Start **
** Activity (main) Create, isFirst = true **
Activity Create
** Activity (main) Resume **
Button clicked.
** Activity (main) Pause, UserClosed = false **
** Activity (activ2) Create, isFirst = true **
** Activity (activ2) Resume **
** Activity (activ2) Pause, UserClosed = false ** <--- home button
** Activity (activ2) Resume ** <--- icon tap
** Activity (activ2) Pause, UserClosed = true **
** Activity (main) Resume **
Button clicked.
** Activity (main) Pause, UserClosed = false **
** Activity (activ2) Create, isFirst = false **
** Activity (activ2) Resume **