We're often dealing with cedar-apple rust here in NC due to the thousands of red cedar and junipers that grow here in abundance. Those combined with the native crabapples and we've got a long term relationship going on between them!
But, on a good note, bpsgarden, the spores require a live host to fulfill their life cycle and your mulch won't be considered a live host. If you like you could let your cedar mulch "rest" before using it. Or just keep an eye out for any fresh cedar galls in it. They'll be brownish/red and look bumpy, almost like they have a bunch of little horns on them.
Normally the apple orchards will choose to spray a fungicide on the leaves of the apple trees, halting the life cycle of the spores. I'm sure that is an option for you as well. Some folks look for the galls on the cedar trees as well but considering the spores will easily travel several miles once they're released that would sure make an awful lot of trees to search out.
Hope this helps.
And Welcome to ATP!~
Shoe