They definitely should have that conversation and ask. If the service you provide is valuable enough, their customers will accept as they'll gain a lot.
You signed an NDA with your customer. Your customer signed an NDA with their customer. They should explicitly ask and figure that out, and then they're given permission to share with you. What they share with you is covered by your NDA.
One way to do it is for your customer to convince one of their customers for a pilot project. The project is successful. Your customer then brings that successful experience to one of their other customers (after asking the customer who participated in the pilot project if they could share that with other customers).
Let's look at the following:
- Vendor "V" has a customer "B"
- Customer "B" has customers "C1", "C2", "C3".
"B" talks with "C1" and convinces them to do project and this requires giving information to "V" because "V", can work some magic. "V" works on the project for "B" on the case of customer "C1".
Once it's successful, "B" can ask "C1" if it's possible to talk about this with "C2". "B" then talks with "C2" about the success with "C1" and "V". "B" onboards "C2".
This works well. Especially when "V", "B", and "C1" can share freely and be on the same calls and emails. In some cases, however, this cannot happen. "C1" has effectively given permission to "B" to share their information and data with "V" for a project lead by "B", but, "V" and "C1" must not communicate with each other.