There are two common ways to talk about altered tunings. It's good to be fluent in both, so you can talk to either type of guitarist. Players who are stubborn about only learning one method, and ignoring the other method, tend to have the most miscommunication with their bandmates.
The first method is to learn the concert pitch or "actual" pitch of your notes. In your case, your whole bass is tuned a step down, so you call your open-string notes A D G C F.
The second method is to transpose so you call the notes what they "would be" called in standard tuning. So you call your open-string notes B E A D G irregardless of the actual pitch that sounds.
It sounds like you have found yourself in a band with a guitarist who only speaks one of these two languages, and can't wrap his head around different instruments in the band using different tunings. You are playing the concert-pitch note F but the guitarist wants to think of it conceptually as open E, because that is the 'normal' tuning from his guitar-centric perspective. From my experience playing with guitarists like this? My best advice is to write your songs out in TAB in his tuning (not your tuning) or whatever is his preferred notation style. Just accept that his tuning is important to him, and if you are trying to teach him a song, move everything on that string by 1 fret to compensate. Meet him on his level.
You might argue 'why should I bend to him?' but in my experience, it is good to be fluent in both musical languages. It clears up a lot of misunderstandings, to see things both from your perspective and the guitarist's perspective.