Well assuming that the gates don't move timezones. But obviously jobs that need to run for a given timezone should be configured to run in that timezone.
no, it would run either twice at the "same time" as it is read out, but obviously 60 minutes apart time duration wise; but this can't be helped as this time "existed" twice in that time zone. Or conversely in spring that time wouldn't happen at all, but the cron job will still run 60 minutes apart time duration wise. But this is the downside of local time, just make sure if you want to open a door at 01:30 local time that that is what you really want, because the unintended consequences could be a bit strange.