Modern gunpowders are totally non-reactive.
That's not quite true. Light and oxygen will degrade them over time and most powder dispensers don't have as tight of a seal as the stock container, and are see-through, so are not the best long term storage option. But as in your case (and in mine), when you are using it and continuously replenishing it there's no problem.
Having said that though, MOST shooters will never notice a difference even with several years of powder stored like that, but it bears mentioning so they can be fully informed. As you stated and I did in my previous post, the biggest danger is that of mixing up your powders.