Yes Lisa-RICCIA is a crossover event song, but Konami almost always acknowledges songs shared between two/three Bemani in events as songs brand-new to those games, and they almost always appear on the OSTs of both games. (With the occasional exception, such as with 532nm.) A recent example is with Zirkfied, which appeared on the soundtracks of all three games it was in (tricoro via the SPADA OST, the Sunny Park vol.2 OST, and the REFLEC BEAT colette vol.2 OST). Note that SPADA didn't feature any BEMANI crossovers from the Q-pro, Mimi, Nyami & Pastel-kun no Minna de Uchuu Sensou!! event in tricoro aside from Zirkfied and Nagisa's "IIDX" version.
If Lisa-RICCIA doesn't count as a jubeat song, then Cosmic Hurricane and the other Tsugidoka songs shouldn't count as a song from any particular BEMANI game either in their respective artists' pafes.