HireRight background check question

I’ve finally submitted my details for a background check after going through some interviews.

Does anyone know if these third party background check companies contact your current employer? I’m worried that my current employer will know I’m looking elsewhere - my worst thought is that I’ll then not get the job and they know I want to leave.

Has anyone had this experience?

usa jobs
usa jobs resume
usa hotel jobs
usajobs
usa jobs federal government
usa job in ksa
usa jobs
usa jobs login
usa jobs gov
usajobs.gov
www.usajobs.gov
usajobs.com
usajobs
usajobs.gov official