When you install Pulse SMS, it imports the latest 250 conversations (and the latest 500 messages per conversation) from the shared SMS database on your device. Every phone has a shared database that SMS apps can use to transfer messages when you install a new SMS/MMS app.
If the messages that you have sent or received from other SMS apps do not display when you open Pulse SMS, then your previous SMS app was not writing those messages to the shared database. For obvious security reasons, Android doesn't allow one app to reach into another app's database to read or write data. Unless your previous app wrote the messages to the shared database, there will be no way for Pulse SMS to display them, unfortunately. This issue is on your previous app's side, not Pulse SMS'.