By default, Cisco switches opt to use Cisco-proprietary version of STP, called PVST+ (on 802.1q trunks), that creates a separate STP instance for each VLAN. HP switches run standard STP protocol, that only has single instance of STP for all VLANs. That's my guess.
To avoid issues with compatibility, you need to configure Cisco switches to use MST, which by default only creates single STP instance for all VLANs. Here is the configuration example for Cisco switches:
spanning-tree mst configuration
spanning-tree mode mst
This should get you to a stage where a single STP instance is running across all your switches.