Does the TFS 2015 server maintain two separate lists of check in policies which are enforced for a team project -- one for the Visual Studio client and another for the Team Explorer Everywhere client? This appears to be the behavior I am seeing.
If I look at the Check In policy settings for a Team Project via Visual Studio I see a number of Check In policies configured. If I look at the Check In Policy settings for the same Team Project via Team Explorer Everywhere I do not see any check in policies. Likewise, if I add a check in policy via Team Explorer Everywhere for a specific Team Project it does not show up if I query the check in policies via Visual Studio.
Yes, this is the correct behavior.
Check-in policies that you define by using Team Explorer Everywhere only apply when you check in by using the Team Foundation Server plug-in for Eclipse or the Cross-platform Command-Line Client for Team Foundation Server.
If you use another client, such as Team Web Access or Team Explorer in Visual Studio, these policies do not apply. Similarly, policies that you define by using Team Web Access or Team Explorer in Visual Studio are not applied when you check in by using the Team Foundation Server plug-in for Eclipse or the Cross-platform Command-Line Client for Team Foundation Server.
More details please refer this link: Configuring Check-in Policies (Team Explorer Everywhere)
You could also find corresponding info from check in policy with visual studio:
Visual Studio 2017 : Check-in policies in Visual Studio 2017 must be set through Team Explorer, tf.exe, or through registry keys declared in the pkgdef of a Visual Studio extension. Policies only apply a single installation of Visual Studio 2017 on your computer. If you have mulitple installations of Visual Studio 2017, you'll need to set the check-in policy on each installation.