In the scehdule, check the value for 'Download required files X Days/Hours before patching starts". That’s usually an issue when trying to set very specific patching times.
I don’t recall the default value for that, but I think it’s maybe…12 hours? When that value is set, the Patch Action is created that many hours before your scheduled installation time. So if you want your job to execute at 12pm noon local time, with ‘download 12 hours before’, the Patch Action would have to be created at 12am; and it would actually be created at 12am in “the earliest time zone on Earth, UTC+14”.
For a tight schedule like that (where you want the Policy to refresh and the Actions to be issued within an hour of patch installation time), you might benefit from using Maintenance Windows. Your best bet is probably to schedule everything in UTC; base the schedule times on the earlier time zone (Standard Time); select the ‘Run within the Maintenance Window’ option on the Schedule; and use Maintenance Windows to unlock the machines at “noon local time” (where “noon” changes twice a year).