Been a while since I played with my HT813 but I think the ring patterns are more for the FXS port ("how the phone should ring") than the FXO port ("the pattern incoming calls ring witih")
I did something similar to you, getting a hardwired condo enterphone to ring through to my PBX then through to my cell. I think it was a call forwarding setting on the FXO port and the call went through straight away. There's maybe a setting for caller ID on the FXO port too - this is usually sent between the first and second bursts of ringing, so you might want to turn that off to get a quicker notification of an inbound call.
Maybe post a screenshot of all the FXO settings?