Standard CTI doesn't work when we put different link in the Provider URL

Hi experts

We were able to integrate our client's telephony (Vicidial - Asterisk based) with C4C perfectly. Unfortunately, they have a requirement wherein their softphone should be embedded in C4C so the agents won't need to switch browser tabs. They want that everything-in-C4C feel. They gave us their link and I put it in the Provider URL bar inside the Live Activity Configuration under Administrator > Service and Social. See screenshot below.

Once applied, the below screenshot shows how it looks like in Fiori. I adjusted the Provider Control Dimensions as necessary.

Unfortunately, when we try to simulate call via the adapter, it doesn't pass through. Does the link "http://localhost:36729/CTIMain.htm" has something to do with this? Please help.

Thanks