When it comes to your credits in the Private mode, your credits are exclusive to you. If you create content on the private mode, your team mode credits won't get affected, and vice versa.
Similarly, if you generate content on the team mode, your credits consumed don't affect your private mode credits.
You can still use the private mode if you only have paid access to the team mode (and not an individual account). Your private account will be available as a basic account (free forever) with 10 daily credits.
Also, team credits are accounted for as a single pool. So, if your team has 5 members with total credits worth 250K words, your credits aren't divided between the members. It's available as a single pool of 5000 credits.
As such, you cannot count the credit usage of different members (though you can check productivity for each member).
The account admin can also access the team credits in his private mode. But the teammates can only access the credits in the team mode (not private).