When I dig an upward staircase it reveals the tile above so I can excavate it and make a downward staircase.
When I build one it doesn't reveal the tile above and I can't dig upwards.
Have I made a mistake or is this a bug? Is the only way around this to dig a new staircase?
So I just tested this out myself -- you've made a mistake, albeit a small one.
You're correct that building an upward staircase won't reveal the tile -- you're wrong that the tile can't be reached for digging a down staircase (or up/down in my case). Just designate the tile directly above the constructed staircase, as normal, and soon enough, one of your miners will come along and take care of it.
The big difference here is that because the tile is not revealed, it will not flash when a miner is pathing to perform the dig job. I'm betting this is why you thought it wasn't working? However, the job still exists, and will be performed normally.
