I think the responses thus far are heading in the right direction, it’s probably the projector. Have a tech go through the projector’s OSD menu, and video or photograph all of the current settings (cell phone video is fine, do whatever is easiest). Then find a setting to reset everything. Sometimes this is a global reset, sometimes it’s per page, sometimes it’s just for color. I’d reset everything. Then play your video and tweak the settings needed from there. sRGB is a reasonable assumption as it uses the same RGB primaries as Rec 709 for broadcast. But manufacturers are all over the map on hitting the sRGB primaries, and the tone reproduction curve.
If it’s still really bad, well, put up some color bars and see if this is a white point problem, or the primaries are just wrong, or what. If it’s an old projector it’s possible the RGB filters are decaying, and there’s not much that can be done about that. Get it as bright as you can and the white point reasonably neutral. The next step would be some way to characterize the projector, and then do a 3D transform of every single pixels on-the-fly to account for the difference between sRGB and the projector – although I can’t tell you what can do such on-the-fly 3D transforms, maybe someone else knows that. Otherwise the alternative is to re-render the whole film and bake the transform into what’s effectively an projector specific video, and I think Premiere can do that these days with ICC profiles.