Why we have s_fid not s_vi cookie for First Party implementation

Hello,

We have implemented Adobe Analytics as First Party Implementation (to our domain). You can see example here: www.stepstone.de
According to documentation, we should get s_vi cookie but still s_fid cookie is set 

Could you please clarify what is wrong and how we can fix it to get s_vi cookie in the beginning?

I checked on my computer, on browsers with clean cache:

Chrome – there are both – s_fid and s_vi cookies or s_fd only

Safari – there is just s_fid what is wrong

Opera – there is just s_fid what is wrong