Timing Closure, LogicLock and Incremental Compilation

"Empty" partitions aren't fully emptied - Quartus will automatically preserve some logic in those partitions. Typically it will be periphery logic or logic connecting to the periphery so it shouldn't be a lot left over.

Regarding timing failures in preserved modules - are all nodes along the path preserved? TimeQuest has an "Extra Fitter Information" tab that has a column indicating whether the node was locked or not and which partition the node belongs to. Often what is happening is that the source/dest are in the preserved partition but the combinational nodes along the path are in a partition that was previously "empty". In general, using this kind of "empty" flow requires some planning to avoid problems closing timing on cross partition paths later on (e.g. having registered partition boundaries helps a lot).