Dynamic Updates of Widget Content using Tags

My business involves a number of team members who each receive reviews for their somewhat different services. So in my case the testimonials are helpful for the overall business but it is essential that my website display the reviews sorted by the dozen or so team members.

I created tags for each team member, tagged the testimonials, and fairly easily set up widgets with testimonials for each team member that worked on the website. However, I'm not seeing a way to dynamically update which testimonials are contained in the widget.

So if a new testimonial comes in I not only have to tag it, but I also need to manually add the new testimonial to the appropriate team member's widget. Is there a way to have the contents of the widget dynamically update when I tag a testimonial? Or is there some other way I should be sorting the testimonials for each team member other than tags that would allow the website to dynamically update when a new testimonial comes in?

Thanks.