Paging procedure is divided into two categories:
1. UE specific:
When an UE is in ECM-IDLE state at MME, and MME receives "downlink data notification" from SGW for the same UE. MME sends S1-AP Paging message for that UE. MME sends couple of critical information need at eNodeB to calculate Paging Frame and Paging Occasion. Paging Frame and Paging occasion both are used to find exact time when UE wake up and check the PDCCH for incoming Paging message.
If you see there is an IE "UE Identity Index value" in S1AP paging message. Actually this IE tells about the Paging frame, in which paging message should be transmitted. Now question is how to calculate paging occasion (which is nothing but subframe of paging frame).
There is a concept of "Default paging drx cycle" which is transmitted within SIB2 and UE specific DRX cycle.
If MME aware about the UE specific paging drx cycle it sends this information inside S1-AP paging message and eNodeB uses to calculate paging occasion else eNodeB will consider default paging drx cyle.
Once eNodeB finish calculation related to Paging Frame and Paging occasion. It prepares the RRC paging message and sends to UE or a set of UEs.
Note: Calculation related to PF and PO is given in 36.304 TS. You can go through it.
2. In General
Whenever broadcast system Information get changed, ETWS notification, or CMAS notification comes. eNodeB informs to UEs immediately. This is applicable for UEs in RRC-CONNECTED mode as well.
Please refer 36.331 spec for more details. If you still have any doubt ; drop a query .