Are you using this app
Call Blocker to try and block the incoming calls? If not, how are you trying to block them?
If I understand you correctly, when you block an incoming call, other callers say that they receive a busy signal?
What I think is happening is that you have call waiting disabled, which means you can only have one caller at a time. So if the blocked number calls and is sent immediately to voicemail, your line would still be in use from your carrier as the voicemail message is played. Even if the blocked caller hangs up, it will keep your line open until the default timeout.
If call waiting were enabled, then even when you are on a call, your phone would ring and you could answer or dismiss the incoming call. In this case as the blocked call kept a line open with the carrier, any incoming calls would still come through. There is no phone solution other than to contact your carrier about call blocking and call waiting options to your account.