Most, if not all of the rest of the band (don't know line-up) will probably be playing at concert pitch. That is, if they're reading music - guitar, bass, k'bds, will read what's in front of them, and it'll come out at that same pitch.
You, on the other hand, have two different transposing instruments - alto in E♭ and tenor in B♭. if your charts are written for those instruments, then you simply play what's in front of you - being careful not to get them mixed up!
The dots will already have been compensated for in the charts.
However, if the whole band is working by ear, you'll have to compromise, and probably bow to the weakest player, who may find it more difficult to change key to be in sync. with the rest.
As user 1079505 suggests, it may all hinge on the vox, who may or may not be able to accommodate much of a change, meaning you'll likely have to play 'in a different key' from the band, and/or what's written.
A look at the line-up, and examples of several preferred keys would mean a more specific answer.
To try to be more exact, as in your question, on tenor, the music will be written out in a key one tone higher than everyone else plays. So, your song in key F will be written - for your tenor - in key G. But the rest of the band will need to play in key F to sound in tune. So, given that scenario, no-one needs to change anything.
F, or playing at concert pitchF? Are any of the other instruments in the band transposing? – Michael Curtis Feb 09 '24 at 20:58