Your sentence is perfectly natural. It's fine to mix tenses in the same sentence if the actions describe different things which are not directly related. In your example, you are in the process of watching a movie, so it's fine to use the present continuous to say that the movie is making you cry. Meanwhile your friend's message is not an ongoing action, so it's fine to use the simple past to say the message made you smile.
Ongoing action vs. one time event, and, aside from the sequence of events and the implied contrast, you choose not to relate the two events. Another example:
I was walking my dog when I found a rare coin lying in the street.
Again, one event was going on when the second event occurred. But it would also be fine to say:
I had been walking my dog when I found a rare coin.
In this case, you want to imply that the two events are related. The first event was ongoing up to the moment of the second event. The past perfect continuous implies that event stopped the moment you found the coin. In the same way, it would be fine to say:
The movie had been making me cry before your message made me smile.