Simultaneously ring with mobile phone switched off

This is the default experience because the nature of SimRing is that it will call your PSTN number first before the Skype client. This is only a marginal thing, but the problem here is that as the phone is off, the mobile provider will divert you to mobile voicemail like you say. This means that the call is considered answered by Lync / Skype and therefore, won't continue to ring the Skype client.

What you will need to do is modify the call forwarding settings on the mobile phone to forward calls to your Skype DDI when not in reach (this includes off). Then calls will be sent through to the Skype client. When the mobile is switched on, or has service, both endpoints will ring as normal.