can't connect smart plug to my router R6400

> I am trying to connect efergy ego (smart plug) to my router (R6400,
> default security settings), and for some reason I can't do it.

   "I can't" is not a useful problem description.  It does not say what
you did.  It does not say what happened when you did it.  As usual,
showing actual actions with their actual results (error messages, LED
indicators, ...) can be more helpful than vague descriptions or
interpretations.

> When I tried to connect the smart plug using my phone's hotspot, it
> was easy [...]

   With my weak psychic powers, I have no idea what you did there,
either.

> Any ideas what should I change to make these devices talk to each
> other?

   Normally, following the instructions in the app works.  That link you
provided includes an "Initial connection issues" section.  Did you
"Reset the socket and try again"?  Is the 2.4GHz radio in the R6400
active?  Are you providing the right wireless credentials for it?  The
list of possible errors is almost endless, especially given no actual
information on what you did or what happened when you did it.