As Gorchestopher H has said
here is also an element of coming-of-age. She becomes involved because her time has come
this is correct as being one of the reason however,
Utena becomes involved because of the way the Rose Bride was being treated
This is half-true. Yes Utena protects Anthy but this is because of Utena's role as the "prince" that protects the "princess" Anthy. However remember that it was not Utena that stopped Saionji in the beginning but Touga. Utena however confronts Saionji after his posts up Wakaba's love confession letter to him on the notice board for everyone to see and ridicule. Utena realizes it's Wakaba's letter when she sees her reaction.
Seeing this Utena challenges Saionji but because earlier in the day the Student Council was told by "End of the World" that a new Duelist would be arriving, he assumes she's the new Duelist and moves their duel to the arena. It is in their second duel Utena protect Anthy from being engaged to Saionji and being abused again.
As for why Utena didn't get involved in a previous semester, we can pinpoint everything to Utena getting involved originated in her seeing Anthy. Why Utena only noticed her in this semester seems to relate to Anthy's omnipresence. In the Apocalypse Saga when Micky is talking to his father, his father passes the phone to the woman who will be Mickey's step mother which we hear Anthy speaking and see her Rose Bride Dress, yet Micky does not pick up on this. Also Mikage is tricked into thinking Mamiya is alive and by his side but not only is his appearance completely different but he is dead and it was in fact Anthy. So it's quite possible that along with being omnipresent Anthy can also make it so people do not notice her.