I think you have this backwards. You meant to say Auto in the other 29 team profile, but Manual during ST (Do teams trade during ST?) If you set to Manual in the profile associated with the other 29 teams, trades will not be offered between the other teams.
There is still a 3 day trade window (versus 'Immediately'), an option you can choose when you begin a Franchise . This means that if you see a trade accepted amongst other teams, (that seems unrealistic) you can just go in and cancel it with the 3 days.
You do however want Manual in the profile controlling your main team.