I noticed the fast spider too - but with Ghost Pots Mod I saw that sometimes if I happened to be doing something near the pot -like drop a seed or water or clip when he appears, he makes an immediate mad dash for the next pot. So, you may get the impression that he always comes out running, which is not really the case at all - he maybe appeared behind the pot and usually they pause a second before they actually start to crawl out between the pots and if, during that slight pause, you do something near, he starts to dash. Without the ghost pots mod you won't see this 'appear, pause, start crawl" scenario. I noticed this also with bugs that crawl out, but also fly up when you scare them - I have had them suddenly fly up from behind a pot when I dropped a seed, simple because I happened to drop it just as they appeared but they had not yet started to crawl to the next pot and scaring them made them fly up immediately - esp the ladybug. All the bugs are "catchable". The Big Hand is not so mean!
_________________________
I love classical music and so do my plants!