I agree with screenman that before and after pictures would be helpful but they don't always tell the whole story either. Something that concerns me is that you said you couldn't see detect an "open hole" for the resin to flow into and you did not see the resin flow into the legs of the star break, yet you decided not to drill in fear of damaging your daughter's windshield. You also mentioned the reason you did not heat the inside of the glass due to the proximity of the headliner.
1) The windshield was already damaged. You either have to commit to doing what is necessary to repair it properly or leave it alone.
2) Although I rarely find it necessary to drill there are times when it is necessary to do a proper repair. In the case of a star break you would likely be able to use a very small bur and drill less than 1mm into the glass to provide the access you need to get the resin flowing. Not only would the end result be cosmetically more appealing than an unfilled star break but more importantly the properly filled break would not crack out.
3) You didn't say what the temperature of the glass was so I can't comment on the need to heat it or not but if you did find the glass needed to be warmed up to optimal temperature it would be best to heat from the outside with a hair dryer rather than from the inside. Not only does that eliminate the possibility of damaging the headliner but heating from the outside requires less heat and is always preferable to heating from the inside. If you attended a Delta Kits training class I'm sure they went over the reason lighters are used in the classroom (noise), but that is not our general recommendation and this time of year most repairs probably don't need heat except to dry out the damage, which should never be done from the inside.
I hope I don't sound condescending, that is certainly not my intent. Your first repair in the real world can be intimidating, especially if it does not go as you hoped it would. It is possible that the Safelite technician was correct and the repair you performed was sound. You might have too high of expectations and frankly I'm impressed that he did not try to sell you on a new windshield. On the other hand, it is also possible that you did not get the damage filled correctly. Learning to see subtle changes in the appearance of the damage, especially in the legs of tight star breaks is extremely important in properly assessing the quality of a completed repair.
I always recommend getting a practice windshield and repairing a number of different types of damage before testing your skills on a customer's car, even if that customer is a relative. The more practice the better but you should feel pretty confident in your skills before you start working on other people's cars. For some technicians that confidence comes with just a few practice repairs and with others it takes dozens to feel comfortable.
Finally, please never hesitate to call Delta Kits before or during a repair. There is often quite a bit we can do to help if we are on the phone with you throughout the repair process. Sounds like you have high expectations, which is good, so get some practice glass and hang in there. We're here to help anytime you need us.