I didn't need to disable STP (in fact cisco doesn't recommend this).Cisco don't recommend this for entire switch, but for interfaces for end devices - PC, Phone etc (that's how I configured it - on phone port). The reason is STP topology change notification.
If I am right turn of STP on phone port(s) (or for any edge device) using
(config)# interface <type>0/x
(config-if)# switchport mode access <----- set port to access mode
(config-if)# spanning-tree portfast <----- disables STP on port
Most likely phone sends DHCP request while port is going through listening and learning phase.
I guess you plugged switch in access ports in VLAN 10 (on one of other switches) otherwise you need to create trunk from one of switches to Cisco switch and set ports for phones to VLAN 10 (if that's your phone VLAN). By default like always all ports are untagged and in VLAN 1. So if you attach switch to access port of your phone VLAN and portfast is configured everything should work.