To be honest Ben, I haven't used TCM in a very long time, so I don't know for sure what or how it's supposed to be done in NX4 or what the dialog looks like. I know it has changed from NX3 to NX4 though. I'm currently only running NX3, but I'm quite familiar with surface modeling and some of the techniques used. I stick primarily with Shape Studio in NX because I feel it's much easier to use and it tends to produce what I feel are more predictable results.
From what I know about NX, Start would be the first string (curve) selected. End would be the last string selected. I assume you have 4 choices for boundary constraints. Just think of start and end like you posted and you will be fine.
Now, the continuity you can assign will depend on the curves used to create the TCM. If the curves aren't G2 (curvature) to the adjacent face/surfaces, then NX will not allow you to assign G2 continuity to the TCM surface. Typically, G1 (tangency) is easier than G2 and will suffice for a smooth transition from the TCM surface to the bounding surfaces, but I can't say it will be acceptable in every situation...that just depends on who is going to be evaluating the model when you're done. If the surface is supposed to be a TRUE Class A, you may wish to invest the time into making all of your curves G2 (curvature), but if there's not a concern about anal studio people picking apart your surfaces, then G1 will probably work. One other thing you can do is if you decide to try building your curves to be G2, you can still assign G1 to the surface and see if G1 will work or not aesthetically. If it looks bad, just edit the TCM and see what G2 looks like.
There are countless techniques that can be used to ensure a good quality mesh of curves BEFORE you actually build the surface, but unfortunately I cannot get into that today, as I need to get home. If you still need help, let me know. Email is fine if you prefer and I'll look for any responses on Monday.
Hope this helps you out a little. Also, read the documentation in NX4 about the TCM....it's VERY informative and may answer additional questions that might come up.
Tim Flater
Senior Designer
Enkei America, Inc.