I've always stained the deck components in conjunction with the building of it. That way you can seal off all four sides of the members after the cuts. It doesn't matter wether you can see the underside or not, they should be sealed all four sides and imo, the end cuts as well.

Thanks for your input! Our deck was just basic pressure treated lumber, so they told us it couldn't be stained for a few months to let it cure. Even though the underside of the deck won't fade from sunlight, I would still feel better if the slats were sealed all the way around.

I should have asked what the wood species is that you are using. It is typically a good idea to let pressure treated as well as some other species dry out before sealing. You might run this by the porches and deck forum as well. There are many pros over there who specialize in decks.

PT wood needs to both dry out before staining and you should apply a wash that removes the mill glaze from the wood before staining. That allows the stain to really take, makes it last longer. Way longer in our experience.

As Sierraeast says, we find it best to do this to each individual piece before assembly (we're in a very wet zone).

Then as each piece is cut, those cut ends get a touch of stain before assembly.

Sounds like that part was missed on yours and a lot of the homes we need to do this on have existing decks with no bottom stain/sealant/protection so the next best solution that I would pursue is to use a cheapo garden sprayer, mask everything and I mean everything, very well, climb under (get a couple of those Tyvek suits from the paint store, we use cheap swim goggles and bandannas for face) and go to it. If you are using solid or even some semi transparent you may have to thin. You will want someone following the sprayer person with a brush to lick up drips and poke into crevices, etc.

Sounds ugly but it goes surprisingly fast.

Maybe a trick I use on ground level decks would work for you?

Just remove the screws, flip the boards stained side down and re-attach.

Now stain the unstained surface?

Wide boards may need to be placed one way to avoid cupping but PT wood isn't the Cadillac of deck boards...if they cup run another screw in to flatten.

I don't think we're going to go to the trouble to stain the underside ourselves - we really don't know what we're doing anyway, and from what I've read, the underside should be ok since it's not exposed to sun. I'm just a little disappointed that our contractor didn't do it, and am wondering if a quote for staining a second story deck would normally include the underside.

... and am wondering if a quote for staining a second story deck would normally include the underside.

A quote only contains what it contains. This is where the consumer needs to be on top of things, stuff like this will only be in the quote if negotiated in. I'm assuming by "quote" you mean "bid" or contract?.

I prefer to have all six sides of a board sealed/stained/painted. But, you know, there are times that would be impossible for any number of reasons so I compromise.

Watch the deck, you can always flip and stain or go under and stain next year if there is too much movement. Its not the sun, its the moisture. The underside will take it up faster and more than the topside. Whether it presents as a problem remains to be seen.

...staining the underside as well as the top is actually worse for the boards because it doesn't allow moisture to get out - does this make any sense?

Not to me. As above I paint/stain/seal all sides if at all possible.

I'd think that standard you are looking for changes regionally, etc. That plus there are contractors who build decks and deck builders who build decks. Both groups will have good guys and not so good guys but if we didn't do our own (we manage rental property) I'd be picking a deck specific contractor.

I suggest contacting this contractor, as this may have
been a simple oversight, by him or his workers.