Or, does it have to be just TBB and that's it?
Yep. You need to match the specified assembly recipe.
Regarding your second part, you have to do the extra mod during the assembly? In other words, you can't do the assembly when you have the mods, then add the extra later if you don't have it on hand at the moment?
You do the assembly first. If you have WK 2 when you make the assembly, you can add a single extra mod any time after the assembly is made.
For example, you want to make a Storm Bolter. If you want to mod it after construction, wait until you have WK 2 before making the assembly. You *could* do any 2 mods leading into that assembly, like BB or TB, first. But when you add that last missing mod, that's when you need WK 2. Following this example, if you build the Storm Bolter, you can add another mod (probably a P or B) at any time, but it'll be the only modification you can make.
Whizkid + assembly interaction is a little counter-intuitive at first, but a little planning can overcome it. Or, you can just live with unmodded assemblies. Most of the Advanced assemblies kick a lot of ass in their own right.