The server will process all ships in system when:
Ships on the galactic map are processed every 6 hours if they are damaged, or immediately if they are undamaged.
If you miss two turns, then on the second turn all of your ships will have orders set to jump out of the system. Even ships too close to planets will jump - usually a ship must be more than 20 hexes from any planet. However, a ship that jumps because of missed turns, within 20 of a planet will suffer 8 random units of damage - this could kill your ship if all habitat is destroyed.
All ships who are entering rip space will do so. They appear on the galactic map. Ordinance they have fired will be destroyed in the system they have left.
All ships, fighters and drones are subject to the ordering below.
All ship actions other than movement,and firing are done at the start of the turn.
Ships move, and as they move they test against mines. Damage is applied but only takes effect next turn. i.e. all the ships movement will complete this turn even though all of it's engines have just been eaten by offensive nano.
It is also now that the remaining 'burn' of the drone is decreased. Should burn reach 0 the drone will die.
Finally, on the return of the tide:
All galactic map moves are made - any that end on an open system will make the ship enter the system (providing they do not break the outnumbering limits).
All ships entering the system do so, ready for that systems next scheduled turn.
When a system is processed a new turn report is generated by the server and you will be notified by email that it is ready. This turn report will show all your ships in every system - those that have just been processed will be shown needing orders, while those you may have already sent in orders for will be shown with their orders. The different rates of play in systems will mean some systems process frequently, while others process less frequently.
As well as giving orders for your ships that need them, you can alter existing orders. There is a chance that the server will process these other systems while you are re-editing them, so it's best to leave those orders alone.