I heavily mulched both my garden and food forest with mulch and later learned that the mulch contained Black Walnut and/or Cenar chippings. As a result, I can tell you exactly which plants are susceptible to harm from it. Is there anything that I can add to the mulch layer that will mitigate the allelopafhic affect of this mulch? I"m going to try Epsom Salt to see if that helps.
Good news all around.
Cedars aren't toxic. It's a bit of an urban legend, based on nearby growth around wild cedars (different species, typically smaller) and lawn Cedars ("dead zone"). However, the dead zone around Cedars is the same as the dead zone around healthy Maples - just an area with very little moisture or sunlight (called "dry shade" and is a pain to deal with without a good sprinkler.)
Here's what I suspect and why:
I suspect that what's affecting your plants is depleted Nitrogen and too much moisture.
When you work wood mulch into soil, two things happen. 1) As decomposition begins, it rips the Nitrogen from the soil and takes a long time to release it back, and 2) it lowers the pH of the soil.
On top of those two things, Cedar mulch is a BOSS when it comes to retaining moisture in the soil (that's why I use it with my Tomatoes, Snapdragons, and Wisteria).
Acidity isn't too affected, just a bit. But the Nitrogen consumption and moisture retention of Cedar mulch can take its users by surprise. You should apply a Nitrogen fertilizer a few days after Cedar is worked/watered into the soil to counteract the Nitrogen rip - on top of the regular feeding the plants get. (This is recommended for any wood mulch, but it's absolutely necessary for Cedar, ime.)
Juglone (the chemical exuded by Walnut trees) is at its least concentration in the wood, but it's still there and still harmful. Considering how expensive Walnut is, how it's processed, and how well-known it's killing properties are; idk if you'll see it in a mulch.
Epsom salt is always a good addition, most soil is lacking Mg. Lime as well. NPK will displace minerals on plant uptake so as long as you keep an eye on your soil's pH you can be fairly aggressive with non-NPK feeding. However, none of that is going to counteract Juglone if there was Walnut in the mulch.
A soil test isn't a bad idea. It's not just a sheet of "your soil contains THIS" - it's gives recommendations on what to add to bring your soil back to a healthy place. I don't know if they'll return any info on Juglone because testing facilities are equipped to test for farmers, and farmers don't have Black Walnut trees growing in the middle of their fields (i.e. they probably don't even test for its presence, but you can ask beforehand, of course).
My recommendation: the next time you need to water your plants, give them some Nitrogen.
Keep a good eye on your soil's moisture. One of the several places I'm using cedar mulch this year is on my upside-down cherry tomato planter (4 plants, each in 5 gallon bucket). I've got experience with cedar and I'm still surprised at how much of a barrier it presents against moisture loss. All my other gardens/containers can be screaming for a watering, and the soil in those buckets will be pleasantly moist.
Don't be so quick to assume its walnut chips or shavings causing the problem. I've used air-dried walnut shavings as mulch, and it hasn't kept anything down more than a store-bought bark.
Juglone is mostly present in roots and leaves, which shouldn't be in a chip mulch anyways. The level in the wood itself is pretty small.
If you did somehow get leaf mulch, Juglone will break down in a couple weeks without a living tree to pump it out.
Cedar is also not toxic to plants, or at least no more so than any other kind of wood. Chips can cause respiratory problems in animals, but that's a mechanical process, and not applicable here. The duff (fallen needles) around old trees sometimes will give people the assumption that it's toxic, but that's because the needles smother out growth, and will make the soil acidic with decomposition. None of these would apply to chipped mulch.
It seems probable there is something else in the mulch you used, possibly a chemical additive. Where did you get this stuff from?
I would say, water well, keep the plants fertilized, and pull the mulch away from the dripline of plants you are worried about. Whatever is causing the problem will hopefully wash away, or at least become diluted in the soil. The only other option is removing all of the mulch you laid.
Honestly, if I were you I wouldn't worry about it too much. Do you know how much of the chips were walnut? I don't believe the wood of walnut has as high of concentration of juglone as the leaves or from the living roots.
It has been proven that plants that are in soil with a high amount of organic matter (compost) are much less affected by juglone. If you soil has a lot of organic matter in it you should be good.
If you are really concerned about it...rake your chips up and allow them to further breakdown and leach any potential juglone out before you reapply, or only use them in areas where you plant stuff that is juglone resistant.
I can tell you firsthand that black walnuts, while I have no doubt of their allelopathic nature, are really not as harmful as many people make them out to be. I have worked in and planted many gardens (including my own) that are very close proximity to large living walnuts and have never had any major problems.