Great question!  You always want to "post" payroll based on the check date because that is when it hits your general ledger.  The final compute is when the job cost records are created.  As long as you are including dates in the payroll timecard (down in the grid) then those entries will show up on a journal by dates.  You don't need to select job cost reports by accounting period.

One of the problems is when I run an over/under report to see if I need to make any accruals.  So I might have a job that we billed in May, but worked on during the final week of May.  I'll have a billing amount of $5,000, but no costs because all the costs are showing up in June.

Another great question:)  

When adjusting for over under billings, you should be adjusting an over billing account for jobs that are "overbillings" (liability account)  and the "underbillings" account (asset)  for those that are underbilled and the difference goes against an income account (you can create a new one called over/under billing adjustments just for that purpose).    If your GL was set up using one of Sage's prebuilt general ledger structures then the over and under billing accounts already exist in your assets and liability sections.

You do not  adjust/accrue actual costs on a per job basis.