I have had the happen on occasion but certainly not all the time. I also don't remember it ever happening when I was younger.
If I'm in a rush but most times no...
That does seem to be part of it, and relaxing and taking my time seems to avoid it.
I think my muscles just relax more when I stop focusing on peeing.
I wonder if there is something in that. Bear in mind I am not a urologist or even a doctor but I am interested and like to speculate. There are two sphincters (muscular valves) in the male urinary tract: the upper (internal) one is at neck of the bladder and just upstream of the prostate. That one is involuntary and opens when you need to go. The lower (external) one is downstream of the prostate and is voluntary, i.e. it opens when you decide to stop holding it in.
What could be happening is that as you get to the end, from habit you close the lower sphincter which stops the flow but, because you're in a hurry, you have done so a moment before the upper sphincter closes. Later, the external sphincter re-opens and by then the upper one is closed. That would cause a small amount to leak out, i.e. the volume of the part of the urethra between the two sphincters.
If this is what is happening, it would explain why being patient would work - it would allow the upper sphincter to close first thus there is no urine trapped between the two to leak out later.
Other variations are surely possible - anything that presses on and restricts the urethra downstream of the upper sphincter and therefore stops the flow while the upper sphincter is still open, but then that restriction is subsequently removed, will have the same effect of trapping a small amount between the upper sphincter and the restriction. After-leakage is mentioned as a possible symptom of BPH, so possibly the restriction could the prostate itself, though I am not at all clear as to why it would present a restriction while going and then relax afterwards. Pressure from clothing could be another issue.