The main question in this situation - do the domains trust each other? EasySSO requires a computer account to operate. This account effectively makes EasySSO appear as a computer to the Domain Controller and the act of logging in using SSO looks like the user accessing this computer.
A computer account must belong to a single domain. So if the user from domain A is trying to login into Jira that uses EasySSO with a computer account from domain B - these domains need to trust each other. This is a pretty usual configuration of domains and if users from one domain of a big organization are expected to be able to access resources in the other domain - this should be like this already.
Your AD admins may be able to confirm the domain trust relationships or this information can also be found by running a simple command from the Windows command line - see our FAQ, specifically:
HOW TO DETERMINE EXISTING DOMAIN TRUST RELATIONSHIPS?
EasySSO doesn't support authenticating users from multiple different domains that don't trust each other to the same service (JIRA). Partially this is because to implement this we need to know where the user is coming from before we start SSO attempt. The only way to do this is based on IP address. This feature is on our roadmap but hasn't even been planned yet.