Intervals.icu looks for max efforts that are long enough to get eFTP (you can set what long enough is in /settings, default is 5 minutes I think). Once it has eFTP it uses your shorter max efforts to estimate W’ by looking for the most energy above eFTP on your power curve.
It only bumps up the “rolling” eFTP number when you get a higher number for a ride and it decays slowly if you reduce training volume. W’ is left alone and you need to capture it from the numbers displayed under your power curve. I have a todo list item to make that automatically updated like eFTP.