I really don't know what to say.
There is a transceiver at each end of circuit. Each receiver sub-system will measure the parameters based on what the far-end transmitter indicates that it is sending. Those determined parameters are then sent back to the far end for monitoring/display, as required.
We are considering the circuit from the CPE end. We know that two separate modem/routers have been used at that location and the same anomaly has been observed when either modem/router was used. I therefore think it is valid to presume that the source of the anomaly is at the CO end. (The DSLAM/MSAN.) Can that presumption be further sub-divided? Possibly . . .
Either (1) The receive sub-system accurately measures the parameters but fails to return the correct values to the far-end until a number of seconds have elapsed.
Or (2) The receive sub-system requires a number of seconds to elapse before it measures the correct parameter values but always returns data to the far-end exactly as measured.
Perhaps what has been observed is nothing more than the cautious operation of an automatic gain control on the receive sub-system of the CO end's transceiver. When the circuit is quiescent, the receiver is set to a minimum gain and only when the circuit becomes active (when CO - CPE synchronisation is achieved) does the receive circuitry increase its gain to the standard operating level. Furthermore, that action may be specific to a particular make and model of CO equipment.
When referring to a transceiver or the receive subsystem, above, I do not mean that part of the CPE - CO link that is the end-user's data channel but the supervisory channel(s) between the devices at either end of the link.
I have not made a study of the operation of typical CO (or CPE) transceivers, so all of the above may be totally wrong. However it does give a plausible explanation for what has been observed.