[1]. https://fas.org/man/dod-101/navy/docs/scmp/part07.htm
https://nationalinterest.org/blog/the-buzz/the-deadliest-air...
[2]. https://www.public.navy.mil/subfor/underseawarfaremagazine/I...
Obviously - they wouldn't be any use if you couldn't tell them to fire their missiles while they were submerged, would they?
real-time communication with subs is probably only necessary to rapidly coordinate a first strike, or to specifically order them not to fire in an ambiguous situation.
Perhaps someone with more knowledge knows if it's possible to give an authenticated order along the lines of "if you don't hear back from us in an hour, launch all your missiles." I've never heard of such a thing but there are at least two former submariners here on hn, so...
They do in the US system! If you don't retaliate immediately then you're dead, and so you can't send the order to fire, so you can't retaliate at all.
In the UK system you don't need to retaliate immediately as authority to fire is delegated to the commander - no magic codes like in the US.
https://en.m.wikipedia.org/wiki/Communication_with_submarine...
The VLF section above that one is also relevant.