Active Directory (AD) integrated DNS zones are not replicated by the DNS server, but replicates through the Active Directory replication mechanism, and uses the same settings for AD replication.
You can trigger replication through Active Directory Sites and Services, or with repadmin.exe on command prompt:
repadmin.exe /replicate target_dc source_dc DC=DomainDnsZones,DC=domain,DC=com
Replace parameters accordingly:
UPDATE: this article has been merged into Configure DNS for Office 365 using DirectAdmin → Configure Lync Online.
A good explanation about setting up SPF-records for domains can be found here: