Yes Xcution's main goal since ever was to steal Ichigo's Fullbring in order to empower their own abilities. To do so, they were on the need of contacting Ichigo without leaving any suspicions at first glance, and this is the reason they used Tsukishima's Book of the End to "hypnotise" themselves and thus, show a non-suspicious face when Ichigo contacted them. What's more, Kugo invented the "Tsukishima's-the-former-leader" story in order to manipulate his victim.