Hi,
I (and a lot of people on this forum), have had issues configuring Policy Based VPNs between an SRX and an ASA. Thank god for Traffic Selectors in version 12.1X46.
This will save you a lot of heartache and issues if you can match them up with the Cisco ACLs on the other side.
http://kb.juniper.net/InfoCenter/index?page=content&id=KB28820