The change here is we want the exahust going to keep going for a defined period after the job is done.
Ideally, have it turn on BEFORE the job begins. 
Although, you could probably make the precognition work by adding a start delay to the first layer a normal part of your workflow…
@rojhan, by tomorrow my setup will:
Automatically start the fume extraction upon job start
Automatically activate my pneumatic blast gates (both intake and exhaust) upon start up
Delay the shut down of the fume extraction
Maintain the manual override of the system
Ok, well, I stated my goals at least. 
@sensor, I will document the wiring for you.
Ok, wow. I did it and I love it. I will draw the wiring up tomorrow. How cool is this. I did have to use a relay to convert the negative signal to positive. But no contactor needed. To listen to the extraction start up and blast gates open with the pneumatic mufflers hissing with the job and then run for two minutes before shut down once the job is complete. Wow.
Good job!!
Was it easy to do?
Reading this dialog is like watching my kids in a candy store, I love it. I’m nowhere near this level, however, it’s inspiring so, Thanks!
Here it is drawn in LightBurn. I have a lot more to mine (controlling blast gates as well as a master line switch), but this is the relevant schematic for you (including a manual override switch allowing for independent operation of the fume extractor and bypassing the necessity for the controller signalling).
If you want to download the LightBurn drawing, I have attached it as well. You may want to enable Filled Smooth to view it (Alt+Shift+W).
AutoExtractor.lbrn (1.5 MB)
How awesome!
Thank you for the effort for the schematic!
And as an added bonus: I also found out what the use is of project notes.
Kudos Jeff!
So, playing around with A1/A2 polarity and S didn’t work.
At least we’re confirmed that using a helper relay to invert makes it work as expected.
If only I had the time to try the solution today…
Anxious to get it working 
SO I have the setup working somehow but not the way I want to.
the manual override works.
the relay sending a signal to Y1/S/25 works as well.
But… when I put my smart relay on function E (Delay on Break) this happens:
It turns the power on after a break for the set time.
And looking at the picture that is also as designed.
I am afraid that there is none of the 13 functions that does what I ask of it.
I want it to be on all the time when operating plus and as soon as I turn it off… delay the relay break for the set time.
Mode E is what you’re wanting. If it isn’t operating properly then check your wiring.
I have a similar set up when power comes on from the controller it pulls the time delay relay in.
Now the time delay relay is waiting for the power to be removed from the controller so it can count down and shut down the two 6" blowers. This shut down delay is set by you. If interested I will get some pictures of the set up and parts. It looks like Stroonzo’s set up is the same you must have an extra relay to control the signal as long as the extra spst relay is pulled in the time delay relay will not count down as soon as the signal is lost the timer starts is count down. Plus you have some extra contacts for some operational lights on your control panel everyone needs more lights.
Rudy
I have to go through the wiring again!
Because at this moment it stays off… until I turn the power OFF and then it turns on for the set time.
Everyday another oppertunity to learn something new
I agree.
The dial is on E mode. Double checked that just now to be sure.
Going to follow the wires again.
I GOT IT WORKING!!
I am not sure what I did wrong… but I took all the wires out and put them back together… and it worked.
I think I switched the polarity somewhere.
But thank you @Stroonzo and @rojhan and @Stan and @Rud
One happy guy here now
Something I thought about today, you should probably put a flyback / snubber diode on the relay coil (maybe like a 1N4007) to suppress the inductance voltage from slapping your controller around.
Illustrated here in a short video I made:
Some relays have this built in. Won’t hurt to add a second one, but no reason for more wiring if not needed.
Well, as you can see in that video that relay doesn’t have it built in (and that’s the exact same relay I used).
Hmm did you notice anything strange in its behavior before you thought of this diode solution?
I did see the diode as well in the ultimate air assist drawing in 2 places.
