Batman & Superman Don't Exist Within Arrowverse
The bad news is that not only does Supergirl not exist within the Arrowverse, but the same applies to Batman and Superman.
Throughout the episode saw portals trying to be created, with the end revealing Barry and Cisco finally making their way through in order to get help from Supergirl against The Dominators.
Cisco says, "I have to say. This is a nice universe you got here."
Obviously from that we are to understand that Barry and Cisco crossed universes to get help from Supergirl, which means the world of Supergirl is a totally different universe than Arrow and The Flash, and means the Tyler Hoechlin Superman (and by chance Batman) is only part of Supergirl.
The good news is that, as we see, Supergirl can obviously still cross over and be featured with Arrow and The Flash.