Q: I've always been told I have to use "since" when referring to time and "because" when referring to cause. Is that true?
A: While "because" does imply cause, "since" can imply time or cause. What does that mean? It means that most of the time these words are synonymous and you can use either one.
Since my dog is so hairy, I have to get its hair cut regularly.
Because my dog is so hairy, I have to get its hair cut regularly.
Both of these sentences are correct. The only trap you have to watch out for when using "since" is ambiguity.
Since we had breakfast, we were filled with energy.
This lets you wonder, were we filled with energy because of breakfast or just after breakfast?