Offset is a correction when the displayed temp is not what the actual temp is. For example, the PID reads 100 degrees but using a known accurate thermometer the actual temp is 104 degrees. You would change the offset value so that the PID would read 104 also. It does not change the process temp (temp inside the box), just what reads on the PID display. Think of it as display calibration. In the MYPIN setup menu it should show "PUF" (or a broken bar simulation of this) when you are in the input offset parameter. Was that the setting you changed and are calling offset? If not, what did the display show for the type of setting you changed?
I assume this is the egg incubator you messaged me about. That would explain the tight band of temps and range of temps you are describing here.
If you can make the box less leaky to heat that will help. Insulation is one way (and recommended if it's not already insulated). I don't know anything about incubating eggs, but if you have any air flow such as in an air inlet and exhaust, that could affect the stability of the system. I would presume there must be "some" airflow.
I went back and looked at some of our earlier messages and I have another suggestion. I would leave the 12v air circulation fan on 100% of the time and not tie it to the PID control. With the fan being off as the temp drops and the PID determines heat is needed, from the way you described the setup, the fan and heat are coming on at the same time. You likely have a fairly stagnant air area around the temp sensor with the fan off. So the sensor may be at one temp with the remainder of the incubator at other temps (temps as in some hotter and some colder in different parts of the box). To leave the air circulation fan on 100% of the time, you would be insuring more even temps throughout the entire incubator and the PID is only dealing with one change at a time (ie, adding heat, not having to deal with adding heat and the now blowing fan moving air of different temps). I think shutting the air circulation fan off with the heating element is contributing to your temp swings and leaving it on all the time will tighten the band up more.
As to the flashing.... That normally indicates there is a voltage being output to the SSR to control the process (turn it on, and in this case apply heat). So you are saying that the desired set temp is "A" and the PID is indicating the actual temp inside the box is higher than "A" and the output is flashing (as in turning the SSR and heater on), correct? Did you change any other values besides offset when you went into the setup menu? Also is the "OUT1" light flashing at a stead rate like an error indicator, or is it pulsing like when the heating element is on? Is the SSR LED also flashing in concert with the "OUT1" led? If it is, then the PID is trying to heat the incubator.
Follow up question (probably should be the first question). Did the auto tune complete? The "AT" light should go out and stay out. Also auto tune is persistent, so did you shut the PID off and turn it back on? It should hold the programming.