In Rumba+ v10.1 or higher, Under Session Configuration, Edit: Parsing there is an option for "Move Cursor After Paste".  When this option is enabled, the "Move Cursor After Paste" option will place the cursor after the last character of copied text.  If the copied text fills the field, the cursor will advance to the next input field.  The input field may be visible or hidden. 

When unselected, the cursor is restored to the position it was in before the text was pasted.