One emerging architecture for hybrid cloud connectivity is "bastion" or "transit" virtual networks:
. This scenario allows you to connect multiple, different cloud networks to a data center using a single hybrid connection. The cloud user builds a dedicated virtual network for the hybrid connection and then peers any other networks through the designated bastion network.
. Second-level networks connect to the data center through the bastion network, but since they aren't peered to each other they can't talk to each other and are effectively segregated. Also, you can deploy different security tools, firewall rulesets, and Access Control Lists in the bastion network to further protect traffic in and out of the hybrid connection.
Reference: CSA Security GuidelinesV.4(reproduced here for the educational purpose)

APIs are typically REST for cloud services, since REST is easy to implement across the Internet. REST APIs have become the standard for web-based services since they run over Hl'-P/S and thus work well across diverse environments.
Reference: CSA Security GuidelinesV.4 (reproduced here for the educational purpose)

In forms of service models, it is cloud service provider's responsibility to maintain security incident and event management(SIEM) capabilities

As with security. compliance in the cloud is a shared responsibility model. Both the cloud provider and customer have responsibilities. But the customer is always ultimately responsible for their own compliance. These responsibilities are defined through contracts, audits/assessments. and specifics of the compliance requirements.
Reference: CSA Security Guidelines V.4(reproduced here for the educational purpose)