Octavian was very much in favor of preserving family values, but he wasn't against homosexuality; Romans of his time didn't even have a concept of homosexuality in our sense. Octavian was against stuprum, "sexual immorality" - or more specifically, sex acts that degrade Roman citizens.

In the Roman way of understanding sexuality, being penetrated is always degrading, unless you're a woman and it's your husband. So Octavian was against adultery, and against Roman men having premarital sex with freeborn Roman women, and against Roman men having sex with freeborn Roman boys or men. But he didn't have any problem with Roman men having sex with male slaves or male foreigners; from the Roman perspective, men being attracted to teenaged boys was the norm.

(The best source on this is Craig A. Williams' Roman Homosexuality.)

I mean, there's no way to tell for sure. Julius Caesar was known to be very promiscuous, but Seutonius (who is the only one I know of who mentions this trist) is known for being "gossipy" if I can use that term. There's no documented proof that has survived that points one way or the other, the only source is Seutonius, who mentions it only to say it was probably slander