Allow me to post something more related to the game.
http://www.nicovideo.jp/watch/sm7257130
At 6:44, H-Shiki is in Heat but while being combo'd by H-Sacchin he does not spark. Any thoughts? I think it has something to do with the combo starting from a throw-property move ie Ex-Air Grab.
You won't spark during a combo if the first hit was something that doesn't cause a spark. What defines that is a little iffy. Double counterhits will never cause you to spark, so if you trade with Aoko starmine while you're in the air for example, Aoko can get a combo off on you that way without you sparking. Throws don't either, but I don't know what determines it exactly, because there's obvious "throws" that will just not cause a spark, but at the same time things like Sion's whip has throw properties (if it didn't there would be no way for the whip to cause the opponent to be in a standing state when they're hit OTG or from the air) and I think that will cause a spark. Other circuit sparks don't cause autospark, and I don't think heat activate does, but neither of those can be comboed off of.
EDIT: I don't actually know why double counterhits are made to not spark after the first hit. Double counterhits don't cause spark because if the trade is in your favor the spark would not let you follow up immediately, and it would screw up your combo. Throws don't ever spark because there could be some really glitchy stuff that would happen if some throws were sparked, and I don't know if the game has a real way of indicating which hits in a combo are from multihit throws and which hits are just from a followup combo to the throw.