Sounds like the drain was assembled this way to get out of the joist situation, which lets face it... sometimes you just have to do. This is a modification of the drain parts to make it work, and although not ideal, I'm sure it's been working alright. I would redo the drain configuration the best way you could, we just want to make sure that we are definitely draining and venting unhindered. I hope I don't get a verbal lashing from the others for condoning this! I have been in the same situation and have had to take the same measure, as there was absolutely no possibility of relocating that joist!
You will need an access panel to make the pipe connections once the tub is in its place.