RTLU (Real time lookup) can tell you whether the phone has been switched on in the past 6-12 hours.
With a SRI the attempt is aimed at the HLR which then interrogates the VLR. When the phone is switched off the VLR is not updated instantly and the IMSI is still stored for x amount of time. This is not a fault but just how it works.
The VLR keep this info until it is advised by the MSC that the sub is absent or has moved location.