First, real publishers don't advertise. It is really as simple as that. No legitimate publisher advertises for submissions because any real publisher is bombarded with manuscripts on a constant basis. Their concern is not to find more. Their concern is to make the barrage stop. If real publishers are looking outside of the slush pile for authors, they look to agents or they go after established writers or celebrities directly. Real publishers don't advertise. End of story.
Second, real publishers don't charge writers money. Real publishers give writers money. If you are giving them money, they are not a publisher. They are, at best, a publishing services company that performs some of the mechanical aspects of publishing for a client. It is the client, and not the services company that is the publisher. Thus the term self-publishing. Notably, such companies do not perform the single most important function of a publisher, which is determining the market potential of a book before publishing it. If they ask you for money, they are not a real publisher.
There are plenty of other ways to check as well. Multiple sites keep track of the industry and report on dubious practices. There are probably different ones for different markets, but https://www.sfwa.org/other-resources/for-authors/writer-beware/ is one of the mainstays.
Finally, there are directories like Writer's Market, the Writers and Artists Yearbook, and Duotrope that list legitimate publishers and put some degree of effort into verifying them. Again, there are probably different titles in different markets.
To determine if a publishing services company is at least honest in their business practices, you would do the same kind of consumer research that you would do before hiring any other kind of services company. Google them, look for reviews, check with other clients, check that they have a physical business address, check how long they have been in business, check with the Better Business Bureau, etc.