The Windows Server Monitor is a different application from the .Net Agent. You will need to disable the .Net Agent in order for your development system to stop sending data to your application. If you don't want to have the .Net Agent run at all on your development system you can alter the newrelic.config file in %ALLUSERSPROFILE%\New Relic\.NET Agent to disable it by changing the following:
<configuration xmlns="urn:newrelic-config" agentEnabled="true">
to
<configuration xmlns="urn:newrelic-config" agentEnabled="false">
This has the advantage of being set globally, but if you want to turn it on and off per application you can add the following in the web application's web.config:
<appSettings>
<add key="NewRelic.AgentEnabled" value="false"/>
</appSettings>