The Prophet of Time is actually Balthazar and everything he said won't make sense until a second playthrough... In fact get used to characters dropping vague out of context speeches onto you that won't make sense until New Game+ I did warn you that this was the Xeno team after all.

Viper Manor simply introduces you to General Viper and his Arcacia Dragoons who you will be seeing a lot of for awhile. Guile has one of the most lackluster stories into sneaking into the mansion and that is kind of the end of any relevance he has in the plot. Granted he's broken as all hell since he's one of like I think three characters whose Lv. 3 normal is a group hitting attack. He's a beast in the endgame.

Pierre has an absolutely hilarious story into V. Manor and I vaguely remember Nikki having a more involved plot since he's one of the games few major players and thus his story foreshadows his awesome father. Sadly Nikki is probably the crappiest of the three you get. I am curious, who have you recruited so far?

As for Dario, since it sounds like you chose to ditch Kid, you will get a better version of the story about him. It's a bit complicated and involves another shout-out/connection to CT.