Fresh cat urine barely smells.
Not "smells a little". Barely smells at all.
The compound responsible for that unmistakable stench — the one that hits you from the doorway — is not in the puddle when you are kneeling over it with paper towels.
Cat urine contains a compound called felinine. On its own it is close to odorless.
Over the following hours it breaks down into a volatile sulfur compound, and that is the smell. The one you notice the next morning and cannot locate.
So when you cleaned it fast, you were not cleaning it wrong.
You were cleaning it before there was anything there to clean.
And the part that was there — the part that actually matters — soaked past the surface while you were blotting the top.