In answer to your question, the above "... on the team that created the exam..." is the only one that feels correct (in AmE).
I don't know whether there's a rule to this uage, but my impression is that if you are part of a collaboration with different people all working toward the same goal, then you are "on a team". Examples are:
"How many players are on a football team?" and "My best friend and I were on the same basketball team in high school."
(Players on a sporting team all work together to win)
"At my previous job I worked on a team that did sales and marketing." and "I worked on a team with scientists who have all won awards." (Sales and marketing teams, and teams of scientists work together to achieve some kind of goal in their line of work)
When you say "in a team," it feels like the only thing you stress is that you're not alone, but there's a group of you.
For example:
"In class today, we worked in teams of four to finish the assignment."
"Do you prefer working in a team or working alone?"
"There were five students working in each team."
In the "in a team" examples, you could replace each 'team' with 'group' with no difference in meaning.
Note also, there's a set phrase of "get/divide/break/split into teams" again with just the emphasis that there's a group of you, not necessarily stressing you work toward a specific goal, as in:
"In lab, we got into teams of three to do the experiment."
"We divided into different teams and competed against each other."
"The coach broke the group into two teams."
Hope this helps!
(not a teacher, just a language lover)