Probably, build configuration WebB has a VCS root that includes files necessary for the build configuration WebA only. If this is not what you expect, try configuring the VCS roots so that only the relevant files go into each build configuration. You could probably use Checkout rules for that.
If the configuration is right to you, please describe it in more detail: VCS settings, triggers and dependencies configured for all the build configurations.
Project Manager (TeamCity)
"Develop with pleasure!"