Global filters only work within one data source. However, actions and parameters can be used across multiple data sources. By creating one parameter and then creating a calculated field for each data source, the parameter control will effect all worksheets that have the calculation on it. I have attached a sample here.
The other option is to use actions. The following link provides further information on this subject:
Hope this helps!
The only problem with your solution is when the user wants to make multiple selections or "ALL" option for the parameter (here its your region column) , he/she cannot do that by using this method.
This worked like a charm! Thanks