Two things:
1. When remote started, neither FOB gives the little green light indicating that it started. Work on yours?
2. Normal starting routine (start button or remote) is that it fires up to about 1500 RPM rpm. Fairly good vibration. After about 15-30 seconds, it lidles down to about 700 RPM and is very smooth. If hit the gas to 1500 RPM sitting still in P, then same vibration. Engine appears to be running smoothly. If start to drive there is no roughness/vibration at 1500 RPM. Similar to yours?