The Scottish people have had a vote on leaving. I'd suspect that they would have much appetite for confirming that they were serious last time, so soon. Or indeed after every decision when the general opinion in northern UK isn't identical to the UK as a whole.
But it's to be expected that certain individuals and parties or even governments will use this as an excuse to push for their personal desires. We hear it from the SNP, we note that the Eire government is claiming profound implications (which, of course, there aren't unless they deliberately create them) and we've yet to hear from Gibraltar (no doubt someone will say that the Faulklands are worried too, soon).
All that needs to occur is for all not to deliberately cause problems and agree no or minimal change to existing agreements.