If you want to sound like a native, you need to change all the verb tenses. It should be "One day the students were having a painting lesson. Everyone began to draw a picture...
I noticed the same thing. This is something I've noticed with my Chinese colleagues; their English tends to avoid the past tense saying "I draw the cat" instead of "I drew the cat". The first phrase would only apply during the act of drawing before its completion.
The story is one I've read in English before, and it seems like this version has been translated from Chinese into English by a Chinese speaker. As for the question, I would write the sentence with 10 as "When I gave it to you, the cat ran away."
I would assume this is a lesson for a lower-level class where they haven't learned conjugation for anything besides the present tense, so the language in the passage is simplified so students aren't faced with too much that they haven't learned yet. I've seen similar things in foreign language classes I've taken.
