My SP is working fine with SSO Circle IDP, do I need to test it with other IDPs to make sure it works fine?

I implemented an SP using Spring SAML. I tested it with the SSO Cicle IDP. I have now Web SSO working fine. My customer is using Tivoli Federated Identity Manager as his IDP.

My question is, is having my SP working with one IDP(SSO Circle) considered sufficient to start the integration phase with the customer? Is the Web SSO process independent of which IDP is used(since SAML is a protocol in the end) with my SP?

Thanks in advance.

Yes - SAML is a protocol so (in theory) that fact that you have got it working with one IDP means that it should work for others.

But you need to take into account that the options may be different e.g. one IDP may have encrypted tokens and the other not or one may enforce having AuthnRequests signed whereas the other may not care.