Why does UCWA return different presentations under different logins?

Question

Microsoft

I'm using Microsoft's Unified Communications Web API to pull presence statuses from a Lync server (now called Skype for Business) into my program. Everything works, only under one account I get all the presents that I see in the client, and under the other - 80% returns as "None", although in the link client I see them as online.
I consulted with the link server admin - he says that the accounts differ only in that telephony is allowed on the first one.
Can you please tell me how to set up a second account on the link server?