Hot sauces that are store bought do not need refrigeration.
If the hot sauces are store bought and not homemade then those hot sauces can remain out of the refrigerator at room temperature.
However if the hot sauce you have is homemade then the homemade hot sauce needs refrigerated or it can spoil within a few hours.
If you're not using the homemade hot sauce within a few hours then make sure to put it in the refrigerator as homemade hot sauce spoils when left out at room temperature for too long.
Store bought hot sauce seems to have some type of preservative in it that makes it last longer even without refrigeration.
I've never refrigerated any store bought hot sauce and it never has spoiled.
But homemade hot sauce has spoiled on me when left out at room temperature.
Even when refrigerated the homemade hot sauce goes bad within 3 to 6 days of making it.
That is unless you can it and preserve it.