Continuing education/Continuing competency/CEU requirements vary from state to state. You only need to meet the continuing competency requirements of your home state license. You do not need to meet the continuing competency requirements for the state(s) in which you hold a compact privilege.
However, while there are no continuing education/continuing competency requirements to renew a compact privilege, the remote state may have a jurisprudence requirement for compact privilege renewal. See state-specific requirements here.