This was a topic of discussion once before that I know of. Someone on this site, and I have no idea who, contacted the manufacturer of the pudding and was told that it should be refrigerated immediately upon opening. I would be very careful about leaving it sitting out, especially if someone else was going to be the one eating it.
Jeanne G, longtime member of the Wilton site, contacted the various snack pudding manufacturers and they all stated the same thing. They were all horrified that these pudding would be used in such a manner. They are only safe at room temperature until they are opened. The only safe pudding type of fillings are the commercial sleeve types where the manufacturer specifically states they can be kept at room temperature once opened.
There should be an older post on the Wilton site from the last year or two from Jeanne G containing these responses.