Cookie persistence with LTM Policies

Hi For our two JBOSS applications we have configured VS with policy:

    ltm policy /Common/POLICY_LTM {
controls { forwarding }
requires { http }
rules {
    POOL1 {
        actions {
            0 {
                forward
                select
                pool /Common/POOL1
            }
        }
        conditions {
            0 {
                http-host
                case-sensitive
                values { pool1.domain }
            }
        }
        ordinal 1
    }
    POOL2 {
        actions {
            0 {
                forward
                select
                pool /Common/POOL2
            }
        }
        conditions {
            0 {
                http-host
                case-sensitive
                values { pool2.domain }
            }
        }
        ordinal 2
    }
}
strategy /Common/first-match
    }

Also we have set universal persistence with iRule:

when HTTP_REQUEST {
        if { [HTTP::cookie "JSESSIONID"] ne "" } {
            persist uie [HTTP::cookie "JSESSIONID"]
        }
}
when HTTP_RESPONSE {
if { ([HTTP::cookie "JSESSIONID"] ne "") and ([HTTP::cookie "JSESSIONID"] ne "\"\"") } {
    persist add uie [HTTP::cookie "JSESSIONID"]
   }
}

We observed, that when we open this two application in Tabs, there is a conflict between cookie form servers. becouse there is one domain, when we open first app, servers set-cookie JSESSIONID, and it's OK. When we open second app in new tab, servers from second pool, create new oen JSESSIONID, and second application work correctly, but first application generate new JSESSIONID.

How to resolve this issue on F5 LTM ?

Regards Tom