Propagating Plants - Where To Cut?

One for @Matt , probably, but happy for anyone to answer.

This is the only longstanding plant I've ever had - only the second to ever last beyond a few weeks. Purchased just before the start of CoVid reached the UK, it's now 4.25 years old which is a remarkable feat by my standards.  [Most of the stalks are getting thinner and thinner, though, so unfortunately its days are numbered.]

Ordinarily, when it gets too long, I cut it in half - above a node to see if any re-growth appears in the lower half (95% of the time it doesn't and the lower half dies) and then re-plant the upper half after cutting below a node.

On this occasion, for two parts of the plant, I cut the upper half off just below a node and re-planted it but forgot to cut close to the node on the lower half - and, on both occasions, tiny new leaves *are* starting to appear which is promising.  My questions are:
* have I been doing this incorrectly all along and this is what I should have done, and leave it be?
* ought I to trim back the ~1cm at the top so that I'm cutting down to just above the node and its newly sprouting leaves?

Thanks.

Thanks, @Matt - very helpful.