The pairings after round 1 are fixed (cannot be changed). I interpret your question to be about how to avoid matches with contestants from the same team after round 1. The answer depends on how many wrestlers from the same team compete in the bracket and the bracket size.
The setting you noticed ("Same team contestants:" drop down list under "File"/"Ladder Misc. preferences...") helps for this. If there are at most 2 wrestlers from the same team in each bracket, set this to "Are not allowed to be in the same half of the ladder". If there are more wrestlers from the same team in each bracket, set this to "Are not allowed to be in the same quarter of the ladder".
When the program places unseeded wrestlers into the brackets, it will adhere to this setting. Wrestlers from the same team will avoid each other until the structure demands they compete.