The UniFlex output drivers are basically switches. You can let them switch the internal power (limited about available: 12V, 1A), or you can use an external supply as you noted, and then you are much less limited, as the drivers can switch 12 or 24V, at much higher currents too (say, 3A each).
The external PS does need to be ground-tied to the UF. See the little downward angle symbol... that is ground. The PS has one, as does pin 13 - so these are tied together, as are power consumers, like your valves.
Your second bullet is actually correct... kinda. You are powering the valves with your external PS, and the signal to switch them is coming from the UF... BUT, if your valve is 24V, then the 12V from the UF isn't going to work, as the valve will expect a 24V signal per the CR03 diagram. So, use your external PS, wire it per your diagram above - that is correct. The valve's motor will get its power from your external PS, and the valves switch signal will be also 24V from the PS, switched through the UF, to the valve. If your valves were 12V, then you could get away without tying the external PS to the UF's pins 2, 3, 14.
Note: Since you are providing a very low current signal, you can wire the PS to just one of the UF's pins 2, 3, or 14 - all three are only needed if switching a lot of current.
BIGGER NOTE: Per the Jumper Wire note.... MAKE SURE YOU DO NOT TIE UniFlex I/O Pin 1 and Pin 2 together while using an external PS... you will smoke the unit!
The external PS does need to be ground-tied to the UF. See the little downward angle symbol... that is ground. The PS has one, as does pin 13 - so these are tied together, as are power consumers, like your valves.
Your second bullet is actually correct... kinda. You are powering the valves with your external PS, and the signal to switch them is coming from the UF... BUT, if your valve is 24V, then the 12V from the UF isn't going to work, as the valve will expect a 24V signal per the CR03 diagram. So, use your external PS, wire it per your diagram above - that is correct. The valve's motor will get its power from your external PS, and the valves switch signal will be also 24V from the PS, switched through the UF, to the valve. If your valves were 12V, then you could get away without tying the external PS to the UF's pins 2, 3, 14.
Note: Since you are providing a very low current signal, you can wire the PS to just one of the UF's pins 2, 3, or 14 - all three are only needed if switching a lot of current.
BIGGER NOTE: Per the Jumper Wire note.... MAKE SURE YOU DO NOT TIE UniFlex I/O Pin 1 and Pin 2 together while using an external PS... you will smoke the unit!