Target Accounts Not Filtering Properties

We are starting to identify and use the Targets object, and I’ve created a Team view of target accounts which I want to encourage the team to use. What I noticed today is if you’re looking at the Task section, the next task is showing task for people outside the Team. This is an issue since I want them to see thier own next task associated with the target client. It also appears to do the same from other properties like “last engagement”. Filtering is not working across the properties.

Am I missing something? I see this as a roadblock if the filtering on the Target object is not filtering across all the properties you choose to view.