This tutorial introduces the letters in an order that makes sense for learning the alphabet, which is not necessarily the same as alphabetical order.
If you're serious about Korean, though, you'll eventually buy a dictionary and will find alphabetical order useful when looking up words. You can also do one of these two exercises:
The table below shows Korean alphabetical order. The top row of table shows the consonants in alphabetical order; the first column shows the vowels in alphabetical order.
Here is a chart of all the letters and their pronunciations.
If you read the following table from top to bottom, left to right, you will see the consonant-and-vowel syllables in alphabetical order. Note that there are empty entries in the table; these are syllables that don't exist in Korean words. This chart is not a chart of all possible Korean syllables (the ones that include a final consonant), as there are over 2500 of them.