According to the regulations enforced by the OFCCP, contractors are required to include language that "all qualified applicants will receive consideration for employment without regard to race, color, religion, sex, or national origin" (the tagline) in "all solicitations or advertisements." So yes, your instincts are correct. The proper language needs to be in place in every advertisement, whether it is social media or another site, not just upon application on the company's website. One can never go wrong including the tagline, so I would encourage you if there is a situation where you may be in doubt, to include it. Please let me know if you need additional information!
You can use this OFCCP audit checklist to ensure you're doing what is required to maintain OFCCP's regulations including VEVRAA, Section 503, and EO 11246. Or request a demo to streamline your compliance and recruiting efforts.