I have a theory that it is like the CT (Charge Time) system in FFTA.
This is evidenced by certain monster skills that have the effect "Damage + CT 0" (E.g. The Lamia's Hand Slap)
So like in FFTA, lets assume every unit has a hidden CT gauge that fills up to 100.
If we assume that each unit's CT fills by a number equal to their speed, plus a number based on their actions in the previous turn (Rough calculations from testing in Clan Trials yielded similar number to the ones in FFTA: +40 if you did nothing. +20 if you either moved but didn't perform an action, or vice versa. 0 if you did both).
When a unit's CT fills up, that unit is allowed to move or perform an action and their CT is reset at 0. However, have CT in excess of 100, due to their speed + action bonus (i.e., from Haste, not acting/moving), the remainder carries over. If there is more than one unit that fills up their CT gauge at the same time, it seems that the unit with the higher speed acts first (I'm not sure what happens with two units that share the same speed).
I assume that the turn order listed on the top screen is a reflection of the above conditions, while assuming that all units simply are not acting when it is their turn, and once a unit moves or performs an action, the turn order is recalculated.
Haste seems to fill your CT at twice the normal rate, while Slow fills your CT to half the normal rate. I've noticed that certain Guest/Monster units in certain missions may be given priority to their CT.