I'm not sure of the details about connecting TISoft to the PLC, but there are similarities to the way it was done with GE's software.
First, if my memory is correct, the product that was known as the Series One Junior was never offered by either TI, Siemens, or Automation Direct.
As to your question of why it takes 10 minutes to go online: The GE software had the ability to try all possible addresses that could be set on the Data Communications Unit. Starting with an address of zero, it would send out a query, wait some period of time, and if there was no response, try the next address (1), and so on...
Could TISoft be doing something similar? The node address is set by dip switches on the side of the Data Communications Unit. Check your manual for the proper setting and set TISoft to try to communicate with a specific address.