There is currently some work on Cloud Aware MPP phones ongoing. AFAIK, that feature is planned for later ths CY. One of the things that are planned for that is the unified call history among all clients and devices.
Until then, your MPPs will only list those calls that they're aware of IIRC. That is if you call someone from the Webex App, it will not be listed in there. Same for Calls on Webex unless they're answered on the MPP.
IIRC, the behavior is also different between the app and the MPPs in case of call queue calls. The MPP will show them only if they are answered by the user but not if another agent has answered it. There are also shortcomings in showing the caller id in case of transferred calls.
I've raised some cases with TAC for that and also adressed it to PM. They're aware of it and as initially said, I was told it should be addressed with cloud aware MPPs.