The usages of the first 「（留学生)との」 and the second 「（交流会がある）との」are quite different.
The first 「との」 means “with / together / jointly with” as in ”財界との関係 - relationship with the financial world,”“オバマ大統領との共同会見– a joint interview with President Obama,” and the second 「との」means “telling sth, to the effect” as in “共同して問題の早期解決を図るとのメッセージ - a message telling (both parties) jointly try to solve the problem.” You need to judge the distinction based on the context of the message.
If you pick up 「との」only by sound, you cannot tell which of the usages of 「との」 fits “together” or “to the effect,” and also whether it’s 殿、都の、戸の, all of which sound the same.