
I am to using both those pieces of gear. Have you set the microkorg midi receive channel? Do that first. This is in the microkorgs manual of course and is set from the midi setting matrix on the 2nd selector knob. And Next to that encoder is the encoder for INT/EXT/AUT midi clock. pretty self explanatory really, but you can set it to both EXT or AUT. I prefer the auto clock, this way envelopes and LFOs and FXs times are all synced to the clock from MPC. but in this case the ARP is not, and you have to set ARP times separately. To have ARP in time you need to choose EXT.
Now just start sequence and send notes to the same midi channel you set the microkorg to receive and you will get it to play with everything in time. easy.
you will probably have record to active track but as the microkorg puts out midi CCs as well from the encoders you can record or pass to another midi device that takes the same midi CCs to. You have to have midi CC on in microkorg and you can also send patch changes to so when you start a sequence it will change the microkorgs patch to the one you want.
Also does sys ex to, and you can even back up the patches this way with the MPC.