Can somebody perhaps enlighten me on this; Are the fumes from mosquito mats poisonous or otherwise
harmful to Tarantulas?
I can't find any info on it elsewhere on the internet.

Yes any airborne poison is dangerous to your spiders as long as it is not in the same room as your spider or draft into the room with the spiders in.

The best is getting a mosquito repellent, a spray on or a roll on.
Just apply the spray outside or in another room away from your spiders.