I've noticed that putting wood chips around the base of my tomato plants seem to make them wilt, but my eggplants seem to perk up with having them around the bases. Why is this?
Highly unlikely the mulch caused the tomato plant to wilt.
If there were toxins in the mulch it would have affected the eggplant as well.
Most likely is there is a coincidental issue with the tomato plant.
It's probably that you just happens to notice the wilting after the mulch was applied but it's likely just a coincident.
Here are a couple of links to reliable sources on the topic of arborist wood chips.
I scanned them and did not find much of anything that would support your concern.
U of Washington, Research and Extension Center: USING ARBORIST WOOD CHIPS AS LANDSCAPE MULCH