Activity switches when opening a program

I’m testing the use of activities and I generally like it. I certainly like the concept.
But what’s a pity is this: I have an Accounting Activity and a General Activity. In accounting, my mail/calendar app is open on a date in the past. When I’m not doing accounting and I open in the General Activity the mail/calendar app, it switches automatically to the Accounting Activity, even if I closed that activity.
I thought that I maybe didn’t pin the app to both Activities (taskbar), but I did.

Is this by design? Or can I fix this behaviour?

EDIT: With Firefox or LibreOffice, if I open it in a different activity, I get a new window without switching to a different activity, So I can have different Firefox windows open in different accounts. With Betterbird, that doesn’t work.
Firefox and LibreOffice allow to have multiple instances running I guess, and Betterbird not.