The short answer is that your idea to copy a numbered list from Miscroft Word seems to be the best answer. Microsoft implies that numbered lists are not able to be generated from Visio -- they essentially say "make your numbers manually, and we'll, uh, align the items for you".
David's answer (which is all you get from Microsoft) is a fine way to get the alignment to be automatic (alignment of numbers you typed in vs. text items) -- but that procedure still asks you to manually create each item's number for list. These numbers you typed won't update automatically if you insert an item into the middle of the list, like it does in Word's numbered lists. And that alignment is mostly only helpful if you have more than 9 items in your list, since items 10+ shift things by another character.
For me, if I was not getting the automatic re-numbering anyway, it was faster to do it all manually: type the number and align it myself using tabs or spaces if desired.
But your method of copying the list from Word works better. Updating the list with new items, once inside of Visio, still don't auto-number for me. But I can paste it back into Word, highlight it all and click on the numbered list button again; and then it is ready to be updated automatically again.