This answer is always up for debate, and varies somewhat depending on where your project is (smoke detctor in supply duct or return duct, over 15,000 CFM detectors, etc).
I think you’ll find the following requirements.
If any of those systems are over 2,000 CFM (system being the combined CFM if it’s a shared space) - you need a duct smoke detector (could use area smoke if you want to meet the exception). And it is this detector that will shutdown the unit, when the unit is actually sensed to be spreading smoke. This sensing of smoke also needs to be communicated to the fire alarm control panel.
If you have a system at 15,000 CFM, then you need to go further and have smoke detectors at each floor branch - which would also shutdown the unit and communicate an alarm when smoke it sensed.
Practically speaking, anything that provides fresh air to the building would be better off being shutdown so the fire doesn’t keep getting oxygen. Anything exhausting the building, especially if it’s a dangerous or flammable, is probably better off staying on.
So final answer, if your VRFs are under 2,000 CFM, and incapable of spreading smoke beyond the enclosing walls, floors and ceilings of the room or space in which the smoke is generated - you should be able to leave them on. But turning them off is probably an improvement if it’s simple enough to implement. If the DOAS is over 2,000 CFM, it only has to shut off when it senses smoke, but if you can add functionality to the fire alarm to automatically shut it off, that is recommended.
It doesn’t mean it isn’t a good design practice to design the fire alarm system to shut down the HVAC systems when in alarm - I just have yet to see the part of the code where it directly states that the fire alarm system should be shutting down air handling units. The main exception to this is when the HVAC systems are also a smoke control system, then these would definitely need very specific control during a fire event.