The "ang" marks the part you already know about, whereas "ng" gives new information.
So in a sentence such as the one in the video given above, if you have been talking about the tourist before and you want to add that he ate fish, you can say "kumain ng isda ang turista".
What if you have been talking about the fish before? In the video, when they said "kumain ang isda ng turist", they changed the story (now the fish does the eating!). But to stick to the original story while telling more about the fish, you can use another verb and say "kinain ng turista ang isda": "A tourist ate the fish".
As you can see, in English we often use "the" for the parts of the sentence we already know, and in Tagalog we use "ang", that's why "ang" is translated as "the" in the flashcards.
Generally, if there is an English sentence with a actor and an object, if the actor has a "the" and the object an "a"/"some", we put the "ang" to the actor and use an "actor focused" verb such as "kumain", because we want to tell more about what the actor is doing. If the object has a "the" and the actor "a"/"some", we add the "ang" to the object, the "ng" to the actor and use an "object focused" verb such as "kainin" because we want to tell more about what happens to the object.
Of course you can have English sentences with several "the"s or several "a"s - in that case you can choose how to best translate it. The above is just a general hint. There should only be one part marked with "ang" or an "ang" form:
I ate a fish: kumain ako [ang form] ng isda.
I ate the fish: kinain ko [ng form] ang isda.
The tourist ate the fish: kumain ng isda ang turista/kinain ng turista ang isda.
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