Amplifier relay issue?

Hi all,

I recently purchased a used Exposure 2010S2 integrated amplifier. Asking for your advice on something I noticed:

The amplifier makes a pop sound (through the speakers) when switching the power on.
However, it looks like there is a relay in it which clicks about 4 seconds after powering the amp on. I would suppose that is the speaker output protection relay, but
what puzzles me is that if I have a source (e.g. the cd player) already active and playing, I can hear music through the speakers
immediately after powering on the amp (no matter if the relay has "clicked" already or not yet).

I own another 2 amplifiers, an Exposure 2010 (a 2000-2001 model) and a Sony TA-FA3ES (a 1995 model).
Both of them have the relay thing which clicks about 4-5 seconds after pushing the power button on, but those would not
play any music before the relay clicks (even if the source is active already). As soon as the relay "click" is heard, only then music would be heard through the speakers.

Given the above, am I looking at a faulty 2010S2 relay or some other faulty component in it?