As to the Fisher Barometer and the effects of season change is the real question here.
Will this barometer need to be adjusted for other weather conditions / season changes throughout the year?
Nice gift!
Gyvate is correct. An aneroid barometer only measures local pressure.
If your console(s) are calibrated then all you have to do is set the needle to the ABS reading. Make sure all the barometers are at the same elevation.
A precision instrument like yours should be set to your elevation/altitude meaning you are setting to station pressure. Trying to compensate for temperature would not work very well.
Theoretically, you could calibrate to Altimeter and add a fixed elevation offset but mechanically, the set screw for precision altimeters is meant for making small adjustments.
You should set your Fischer to read station pressure which is equivalent to ABS in the FIne Offset ecosystem. Your barometer was probably calibrated at the factory - maybe at 200 meters? You will need to move the needle to calibrate to your own elevation.
If you feel that your consoles are not accurate enough, you will need to calculate the ABS(station pressure) for your aneroid barometer at its working elevation. To do this you can calculate your REL offset and subtract this from the Altimeter reading at a close-by airport.
EXAMPLE:
Altimeter reading (at the airport) minus REL offset = Station pressure (ABS)
Basically this is the same procedure to calibrate an Ecowitt display console except we are interested in ABS rather than REL.
For better accuracy redo this procedure the next time when Altimeter = 1013.2. To check calibration, add the REL offset to your current needle reading and compare it to the Altimeter reading at the airport. They should be close.
See the link (in my signature) to the barometer section in Gyvate's wiki for more info.
PS use the sensorsone web site to calculate the pressure difference (REL offset).
Edit: You can also use the Altimeter to Station pressure calculator to directly convert any Altimeter reading to station pressure without the math.
See
https://www.weather.gov/epz/wxcalc_stationpressure