The "skipped on restrictions" notice is actually related to the amount of data that Finalsite is pulling through your integration. While the error is somewhat generically worded, it really just means that if there are more than 500 records pulled on an individual sync, that sync will be delayed until the early hours of the morning. This is designed to help the servers balance the load imposed by data processing - in other words, we'll put the hard stuff off until late at night so that your website stays snappy for visitors during peak hours. If the sync does not run completely overnight, just let us know in Support and we can have a look at it.
It is also worth mentioning that if you need the sync to run right away so you can check for errors, you can always contact us in Support and we can force the feeds to run manually.