'Provided that' followed by two conditions
Use and that when confusion might result from the use of and alone.
With your example, one might read:
Manchester United will win the title on Saturday, provided that Aston Villa beat Liverpool and Arsenal...
...thinking that Aston Villa must beat two teams, Liverpool and Arsenal; upon encountering the word "beat" again, the reader might become momentarily confused, and have to start the sentence over again. (This is an example of a garden path sentence.) By using and that instead, you eliminate that potential confusion.