Are You Responsible for Third Party ADA Compliance?
Its extremely common for websites to utilize third party widgets, plug-ins, and systems that may present ADA legal exposure to you.
Generally the rule of thumb is that if you're looking at the page with the item in question and the url includes your domain, then its part of your website and is therefore you're problem. You cannot offload liability onto vendors (including your developer) or third parties if it lives within your www.domain.com.
A common example would be a booking engine on a hospitality website. And here there are two different scenarios that would be treated differently.
In case 1, the booking engine has a widget where, you pick your check in dates. When you hit submit, you're then taken to a separate website: yourcompany.bookingengine.com or bookingengine.com/yourcompany. In either case, you've been taken to a separate site, so with exception to the little booking widget residing on your site, any off-site accessibility issues are those of bookingengine.com.
In case #2, when you submit your checkin and departure dates, you're taken to booking.yourwebsite.com or yourwebsite.com/booking. In this case, the booking engine lives within your domain. Therefore, its ADA conformity is your problem.
As part of an ADA WCAG compliance audit, these will be identified and you'll then need to either work with these companies to make their systems ADA-Friendly, or you'll want to find a new vendor who can.