Ritsu has Solomon's Ring -> Ritsu has control over all the demons -> Ritsu has time to influence the demons and gain their favor
Ritsu releases some demons from their contract + Ritsu still has the demons' favor = Ritsu has control over some demons without the power of Solomon's Ring
Ritsu was stabbed in the back but he looks fine right now, which proves that Ritsu does have some control over the power of some of the demons regardless of Solomon's Ring.
Couple that with the fact that the new owner doesn't know the current state of the demons' powers, and the fact that Asmo-tan is practically useless, they believe that Ritsu is still currently very powerful and is a threat to them as they will try to take back Solomon's Ring.