QT a tarantula from a python?

Just rescued a tarantula...I'm certainly keeping it quarantined but are there specific concerns?

i know both are suseceptable to mite infestations, I wouldn't have thought them the be cross species mites but quick google searching shows results of people talking about cross contaminating snake rooms with tarantulas...

Both my animals are new and on QT in different rooms and ideally will remain there.
I trust the snake's healthy, it's from a local breeder, his snakes where well kept, and is obviously in fine shape...the tarantula was sitting next to a trashcan downtown...in a Tupperware...I couldn't just leave it!

Feel free to give any advice, or tell me I'm an idiot or whatever...
Thanks in advance!