Jerry, I also use the AC in the zone we are not (front AC when sleeping, rear when we are awake to keep the noise down) I noticed we have a delay in the front AC, when nothing starts (no fan or compressor) for a few minutes, but the rear unit seems to turn on immediately. I don't remember if you have the heat pump or not could, it make a difference in the operation.
I replaced the thermostat and the front AC about 3 years ago, so I am probably configured differently. I know there is a control board in both units, the rear slaves off the front. So I would look at the Tstat and both control boards (I think they are the same board, just optioned (jumpered) differently. Call/email me if I can help.
Kudos on being in an area where you need the AC, we are in the 60's during the day, but mid 30's to 40's at night (got to 35 last night, but we are due 75 on Saturday.
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Dave, Bobbi and Fenway
2005 38' FDTS Alpine Limited, 2016 Jeep Grand Cherokee Limited
Cape Cod, MA