DrX Cycle is actually negotiated between UE and eNodeB.
So if the UE 's drx cycle is less and if thats accepted (in the TAU accept), then thats the time in which eNodeB can schedule the page for the UE.
For ex: default paging cycle in LTE is 1280ms, if an app requests for 320ms through modem , then it would be negotiated with eNodeB, If eNodeB accepts it, then eNodeB can schedule the page for this UE once every 320ms. (at which time UE also wakes up once every 320ms)