"It's easy to remove any spider from your pot, just turn the pot sideways and use a jet of water. I also use a large piece of toilet paper when handling big spiders. Soft enough to catch them, but not to crush them. Then you can let them go in front of your house, and they find a new home. Actually, my favorites are the black tarantulas, I've found a few in the past. But I'd never kill them. Beautiful creatures."
To pull you down off the self righteous stool

, the pot weighs 150 lbs. I can't simply lift it and use the water without risking the tree. It is on a three foot tall stand. If it managed to slide off the stand I'd risk losing a $2,000 tree and a $300 pot... I sprayed underneath with a hose, but the spider retreated into the drain hole.
FWIW, I had a friend who owned a pet shop who imported all kinds of stuff back in the early 1970's, so I became pretty famliar with all kinds of exotics. Met one trucker who kept two seven foot inguanas named "shirly" and "bubba" in the sleeper cab of his truck. Tarantulas don't bother me. Had a large-red legged tarantula (not the sissy ones you're picking up with a tissue

) along with assorted boas, pythons, and dozens of natives snakes when I was younger. I handled newly-collected South American tarantulas with a glove as they could be "bity."
If you lived in Texas, you'd be making daily trips to the trail head with buckets of scorpions and wishing them all dead after you're stung six or seven times putting your shoes on in the morning...
I'd LOVE to see what you'd make of fire ants...