You're right that she likely ought to have kept quiet until she could assess her new surroundings... that's probably taught to all combat soldiers, with extra training for a small precision team such as the one Vers was one;
a team of 6 soldiers inserting alone on a hostile planet to carry out a secret recovery mission of a Kree spy is probably quite elite... like a SEAL team element-level of elite.
So this is probably a case of either the studio not having a consultant for these matters or of the plot being more important than the realism here.
In-universe, it's likely that most planets in the regions affected by the Kree-Skrull war are probably planets that are sufficiently advanced to be worth fighting over. A planet with a primitive civilization like Earth's is probably not on anyone's radar (in a manner of speaking).
Also, Vers learns that the Skrulls are seeking a scientist on C-53 (Earth) who is working on a lightspeed engine, which is incredibly advanced technology; it's something neither the Skrulls nor the Kree have access to (they have to use jump points, similar to what is shown in Guardians of the Galaxy 2).
When Vers hears about the lightspeed engine, she probably assumes the planet this mystery scientist is on is pretty advanced, considering a lightspeed engine is tech that is significantly beyond even the Kree Empire. So it makes sense they'd also be aware of the existence of other species and recognize the Kree Starforce name even if they're not part of the Kree Empire.
Consider also that she had a universal translator in her suit that enabled her to ostensibly understand and speak with other species without difficulty. When you can easily communicate in your native tongue with a stranger, you tend to make a lot of assumptions that they understand or are at least familiar with your shared culture, and not just the words you're saying... it's probably the norm for her to land on a new planet and talk to locals who are aware of the Kree Empire (which spans many planets and species, according to various movies).
To analogize it, imagine it's the height of World War II and you're a pilot flying in a naval battle. You get hit by some flak and crash into the ocean, but survive. You wash up on a beach somewhere. This beach is on a small, remote island with a primitive civilization (if that)... you find them and ask who they're loyal to; Axis or Allies? They're probably going to look at you with the same bewildered look that the Rent-A-Cop gave Vers when she walked out of the Blockbuster.
It's also probably worth pointing out that she was
born a human and lived for ~20 years on Earth. She probably felt unconsciously "at home" on Earth, and felt that they must know of the Kree because that's been "home" for her for the last 6 years.