The SIP phone is responsible for echo cancelling echo between its speaker and microphone. The SIP to PSTN gateway is responsible for cancelling echo from the PSTN side. So the phone in this case the phone is the phone on the Asterisk side of the call.
There are two ends of a call, and both can produce echoes. The ITSP is responsible for stopping your user hearing echoes that arise between the speaker and microphone on the cell phone.
Echo cancellation isn’t needed on circuit switched connections, at least not within a continent, because the echo time is short enough not to be objectionable, unless it is very strong, as might be the case for a speaker phone, although they often use VOX, rather than echo cancellation. To work well the echo canceller needs to be as close as possible to the source of the echo.
It sounds like the ITSP is handling their echo cancellation responsibilities effectively, as your agent isn’t hearing echo.
(The only time that Asterisk would normally get involved with echo cancellation is when using DAHDI, as that is connected to circuit switched connections. Although you can use software echo cancellers for that, it is better to use interface cards that handle it. You are not using DAHDI, and if you were, it would be in the ITSP role, not the SIP phone role.)
VOX = voice operated switch, i.e the phone disables the speaker when it detects that the local user is talking.