So, this report is interesting but may be misleading.
First, this isn't a shocking number. Now that the OP has double-checked their numbers and given the link, it says that "between Feb. 15 and June 21 of this year.... 212 people in 44 states had been infected". But if this trend continues (212 people in 44 states every 3 months) nation-wide the number would be less than 900 in a year. Since the count begins in february, not january, it doesn't even take deep cold months into account when salmonella infections from handling chickens and their equipment are less likely. The article states that last year we had 1,120 cases, a record high. That means the current number of salmonella cases is going DOWN from there, not up.
(I will admit, it's much higher than in, say, 2012 when back yard keeping was less and really just starting and the number was 330ish.
https://www.cdc.gov/salmonella/live-poultry-05-12/index.html)
It also does confirm that;
"Of those sick, 72 percent of people told the CDC that they had contact with chicks or ducklings in the week before their illnesses started", which probably means that those cases WERE backyard poultry related... But...
"Each year in the U.S., about 1.2 million people are infected and 450 die from salmonella. Food is the source of about 1 million salmonella illnesses and 380 deaths each year."
So... Around 1000 cases a year, out of 1,200,000 are from back yard poultry, not from eating their eggs but DIRECT handling of the birds, of which they can only confirm a link to 72% of cases...
Certainly we can do better, as a community, to learn and establish better practices. We can do things like limit immune compromised individuals around our birds, use the vaccines (which they use in Europe with overwhelming success!) and remember to practice good hygiene, especially around immune compromised individuals. We can even do things like feed certain supplements to try to reduce the incidence of salmonella in your chickens.
This matters because on a per-capita basis we have higher incidents of illness.
But over-all backyard chicken illnesses are a drop in the bucket compared to other sources.
So the claim that "Backyard Chickens Are Spreading Salmonella to People", which is the title of the article, may be technically accurate but is misleading in it's tone and statement. And while I can understand addressing this issue (an increase of 300-400% of cases in 6 years is nothing to sneeze at), I wonder why they aren't also focusing on the rest of the vastly more likely ways to get salmonella more intensely.
I also worry this article seems to emphasize the fact that it's back yard chickens, with very little specific info on how to have safe hygiene practices around chickens that isn't common knowledge. (Don't lets kids handle chickens, wash your hands, don't let them in your house, have chicken shoes, etc.) They don't even TRY to mention the vaccine, for example, or foot covers, how to properly sanitize surfaces in your coop, dietary supplements to naturally reduce incidence of salmonella, etc.
So I would take this seriously, but also with a grain of salt. We have more people handling chickens now that aren't wearing full disposable suits like many CAFOs have. This is a concern we can address (probably not effectively through the means that they list), but is probably not a huge deal in the grand scheme of things. At least not yet.