3 different default browsers on one pc, but only once login?

[trium 0]

I have tried a little with the change between 3 different browsers as the default. (all on one computer)

for example:
1.) I log in via Agomo service and Firefox as the default browser with email and password, and then log out.

2.) 2 minutes later I log in with Agomo service and IE11 as the default browser (this time I dont need email or enter the password!)

3.) next time i log in with Agomo service and IRON (chrome) as the default browser (again, I dont need email or enter the password!)

should that be so?