In FTM, the sort fields are primary, secondary, and third, depending on the (inverse) order in which the column headings are selected.
I'm not sure what governs sorting in the on-line trees, but try this:
Use a Fact Name before "D(eath)" - for example: Address, with the same date as the death date. Does it come before Death in the on-line tree? That would suggest the secondary sort is the FACT NAME. That might mean the third sort would be the Description field.
I don't think FTM or ancestry allow time of the day in the date field (ie can't tweak it).
Maybe an enhancement request is in order?
On the other side of the coin, I am annoyed when FTM beeps at me when a fact is after the date of death. A lot of things can happen after a date of death, including burial, birht of a child (for a man), pension, proof of a will, etc, etc.