What's causing the sewer to back into the tub?
It turns out that there was a partial blockage in our drain between the DWV and the main sewer line.

Because it was a partial blockage, some water could drain, but when there was a lot of water, and especially solids going down the drain, the line got blocked, and plunging opened a smaller hole in the blockage.

We called our water department and they brought out an inspection camera and shoved it down the drain. We couldn't tell what the blockage was, but it was right at the end of the line. They stuck this bladder thing on the end of a hose and fed it down the line, hooked the other end up to our faucet, and turned the water on. It produced a bunch of pressure and forced the block out through the main sewer line. No clue what the block actually was.