Help using Relays with greenhouse

my fundamental problem right now is to keep my OUTPUT for the condition used at HIGH for 60 sec?

"When any of the outputs are turned on, it should remain on for a minimum of 60 seconds, even if the measurements determine that it should turn off sooner."

I believe that you enter the response loop correctly every 60 seconds, but it looks to me like your outputs will remain HIGH once they are turned on and never turn off, as they are never written LOW.

You need to define conditional tests to turn the relays off, just like you have tests to turn them on. Or perhaps, in the six existing conditions you can turn something off. As said before, you need to sit down with the paper and pencil and write out the conditions when you want certain relays on, and when you want them off. At this point you seem to know how to tell the Arduino when to turn them on and do that every 60 seconds independent of the measurements and display.

//Sensory responses
    
 unsigned long currentCycleTime = millis();
 static unsigned long startCycleTime = 0;
 
 if (startCycleTime == 0) {

  if (t>=28 && h>=85) {
    digitalWrite(AuxFanPin, HIGH);
  }
  else if (t>=28 && h<=85) {
    digitalWrite(MainFanPin, HIGH);
    digitalWrite(HumidifierPin, HIGH);
  }
  else if (t<=28 && t>=19 && h>=85) {
    
  }
  else if (t<=28 && t>=19 && h<=85) {
    digitalWrite(AuxFanPin, HIGH);
    digitalWrite(HumidifierPin, HIGH);
  }
  else if (t<=19 && h<=85) {
    digitalWrite(HeaterPin, HIGH);
    digitalWrite(HumidifierPin, HIGH);
    digitalWrite(MainFanPin, HIGH);
  }
  else if (t<=19 && h>=85) {
    digitalWrite(HeaterPin, HIGH);
    digitalWrite(AuxFanPin, HIGH);
  }
  startCycleTime = currentCycleTime;
 }
 else if (currentCycleTime - startCycleTime > 60000) {
  startCycleTime = 0;
 }