I'll share with you what I feel is as accurate of information as I've been able to ascertain over the past 29 years.
The market is currently flooded with LVP/LVT products that are primarily sourced from Asia (China, Vietnam, Malayasia, South Korea, and most recently India). The large manufacturers of these products work with manufacturing partners in those countries to produce their products. There are different models that these manufacturers follow. Some provide the manufacturing plant with specific specifications and have "boots on the ground" in those plants making sure that the specifications are being met. Some go to the manufacturing plant and say "give me what you make standard and put these patterns on it". Some oversight, but they primarily rely on the honesty of their Asian partner to manufacture the product to the emissions standards required. Last, there are an absolute glut of small importers, primarily larger flooring retailers here in the U.S. that make contact with an Asian partner at a trade show here in the U.S. and there are Asian manufactures who have "turnkey" operations where they will provide you with the product, do the marketing under your trade name, ship the product, and so on. These guys have very little "skin" in the game. They are simply paying to put their name on the box. Then they portray themselves, pretty stealthily in many cases, to be the direct manufacturer of the product. In trying to answer questions for customers as a resource, I've found some of these guys whose "Corporate Headquarters" when googled is a package receptacle at a UPS store in a strip mall in Georgia.
Most major manufacturers (Armstrong, Mannington, Mohawk, & Shaw for sure) manufacture their products to meet SCAQMD (South Coast Air Quality Management District) standards. These are the California regulations that govern VOC's for that state. In order to sell any product in the state of California, you must comply with their minimums or you simply cannot sell products there. These standards are more stringent than the federal standards, so essentially they are the DeFacto standards our industry complies with. No one's going to not try and sell products in the 5th largest economy in the world, right, wrong, or indifferent.
VOC's in LVP/LVT primarily come from the esters (oils) that are used in the product to provide flexibility. Thus, going with a "dry-back", also known as a glue-down, product will have more (esters) than a rigid product such as an SPC or a WPC.
If we look at a fairly common formulation for glue-down LVP, in many cases these products are going to be 70-90% PVC and the bulk of the remainder will be binder and filler (primarily clay). SPC is nearly the opposite with a 15-20% PVC content and the remainder being stone dust (typically limestone but other stones are also being used such as marble). WPC is kind of between the two at about 50-50, but WPC typically has air entrained into the core to provide sound deadening and a thicker, but lighter product.
Since esters form week covalent bonds that can be broken leading to a release of VOC's, then going with a more rigid product eliminates the potential for VOC's to occur. BUT, it is critical to remember that with the manufacturers I've listed, none of them come close to the SQAQMD minimums and in many cases the amount of VOC's from the product are nearly unmeasurable.
I would also be remiss if I didn't add that there are companies who manufacture these products with non-PVC alternatives. Many of them are European manufacturers who take a different view of PVC than we do here in the U.S. However, my experience with those products has been that they have their own set of issues that can cause problems and many of them don't have the sustainability of the products with PVC and must be replaced much more often.
I can try and provide further information if you have specific questions, but hopefully this gives you enough to make a decision without fearing your decision might impact your health. Trust me when I say that there are a mountain of lawyers who would be suing these companies into non-existence as well as FloorScore if the testing was being "fudged". Google Lumber Liquidators Cancer Lawsuit and you'll see what I mean.
…. I have a customer looking for indoor, outdoor for his back porch, but I’m apprehensive to sell him a chemically laden one. It won’t grow mold but it may not be too pleasant eating breakfast in there.
…. Good luck on your search 
Rocket Man, and all the science I don’t understand, it’s just my job five days a week 
