The Virtual Environment you're using isn't leaking, and it isn't compromised. Virtual Machines do virtualise an ISO image to provide a virtualised OS environment which you can use to separate actions from affecting your Host environment (the Guest environment is the virtualised one), however the Virtual Machine will still need to store data for it on the local Host. This doesn't mean malware can drop within your Guest environment and then have the dropped files executed on your Host, it simply doesn't work like this. It neither means the software executing under the Guest environment can access the Host.
It's normal for security software to be able to intervene like you are querying about. This is an indicator that your protection which is active on your Host environment is working correctly, but also that the security software solution you're relying on has well-made and good technology behind it. You can try white-listing the Virtual Machines processes and see if that helps, but I'd suggest not doing this.
The web-protection component of your security software should also be able to intervene the connections from within the Guest environment to block malicious URLs it would normally flag as-is coming from your Host. This would be because they tend to rely on a networking device driver and all connections being performed within the Guest environment must pass through the Host to be carried out, and thus will pass through the security software interception.
ESET and no other vendor which can intervene with Virtual Machine file-system/network operations don't do anything additional to intervene with it. Its to do with how the Virtual Machine software works.
