"The problem I'm having is that the tip section doesn't seem to want to insert all the way into the handle section. Do I need to loosen the phillips screw before inserting it?"
It sounds like the expander plug is already in expanded mode, i.e. all the way down the screw toward the carbon body of the tip shaft. To insert the tip into the upper section, turn the expander plug counterclockwise until it butts up against the head of the screw, then insert into upper section. It should go in easily.
"Also, what's the secret to adjusting these right in the field? There have been times when the poles wouldn't tighten down just right, such that the top section would just spin round and round."
Since your expander plug is new and assuming both the expander plug and inside of the upper pole section are dry, you may have some wear on the inside of the upper pole section if you always set the pole to the same length. Try pulling the tip section out a little ways and attempt to tighten again. If it doesn't work, repeat until you get it to grip, then loosen just a little, push it in a little and retighten until it grips. Repeat until you have the pole set to the desired length. Worst case, pull the tip section all the way out, loosen the expander plug just enough to allow it to insert in the upper section, tighten until it grips, then proceed as above until you have the pole set to the desired length. It's tedious, but sometimes that is what you have to do. At some point in time, the expander plugs will start to show a "wear" ring about midway down the plug, and this process will get really tedious. Then it is time time to send the tip section to GG for expander replacement. They used to sell the plugs, but now you have to let them do it.