I just assume that it was time dilation due to editing. The actual journey was much longer. Don't think about it too much cause then you'll start to wonder how long that song actually is, and then you'll start to question why anyone randomly breaks out into song to begin with, and how everyone seems to know the lyrics despite being complete strangers.
I was going to rip on taking a cartoon too seriously, but then I remembered getting annoyed at superwhy, which is an ABCs show for toddlers. They had an episode where they landed on Saturn, and it was sandy. I had a to give my then 2 year old an impromptu lesson on what a gas giant was and that her favorite show was fucking wrong. I was so irritated that an education show would do that lol.
Aladdin's exact words were "Genie, I wish for you to make me a prince." I always assumed that that meant that the wish merely caused a compulsion in the Genie to use his "standard," non-wish-granting powers to make Aladdin as prince-like as possible. If he'd instead phrased it as "I wish to be a prince" then it would have caused reality to alter to give him a genuine royal lineage.