Hey, so the way this works is the same way the other PVE plugins work - it allows Convoy and Sputnik to fully dictate what happens in those zones. So you should be able to adjust the rules in those plugin configs (I'm just assuming, I'm not sure what their config look like).
The only thing that WarMode does is have it display the mode when you enter those zones, and the mode that is displayed is entirely cosmetic - as like I said those plugins control what happens in their zones. You can change what mode is displayed when you enter them though, by default it shows PVP, but in the WarMode Admin Panel you should see a setting on the right for both Sputnik and Convoy (if you have them installed) to enable a different mode to be shown.
For example, if you want it to show PVE instead, you can select PVE in the admin panel, and then on the right under PVE Settings you can set it to true for Sputnik and Convoy. If you do this, it will display as PVE when you enter them.
You could also in theory create a new mode that is purely for this display purpose if you wanted and call it "Sputnik" or "Convoy".
If this still doesn't help for your situation we can discuss if theres some alternative that can be done.